finite element solution of the stokes problem with dominating coriolis force abstract the objective of this paper is to present a finite element formulation to solve the stokes problem with coriolis force this force results in a skew symmetric term in the weak formulation of the problem that deteriorates the stability of the standard galerkin finite element method when the viscosity is small we show that the stability is worsened due to the presence of the pressure gradient to enforce the incompressibility of the flow the relevance of this effect depends on the relative importance of the viscous force and the coriolis force which is measured by the ekman number when it is small oscillations occur using the galerkin approach to overcome them we propose two different methods based on a consistent modification of the basic galerkin formulation both methods eliminate the oscillations keeping the accuracy of the formulation and enhancing its numerical stability

explicit residual based a posteriori error estimation for finite element discretizations of the helmholtz equation computation of the constant and new measures of error estimator quality abstract this paper continues the study of an explicit residual based a posteriori error estimator developed for finite element discretizations of the helmholtz equation in the context of time harmonic exterior acoustics problems in previous papers 1 3 the error estimator was derived and subsequently applied to h adaptive computations of model problems in two dimensions in the present paper a methodology is established for computing error estimates these error estimates are then analyzed in detail the error estimates are made possible by computing the scaling constant which exists in error estimators of this type in our case this constant is difficult to obtain an algorithm for computing the constant is described it is noted that the error indicators used for adaptive computations do not require knowledge of this constant several measures are used to analyze the quality of the error estimates providing a complete description of the error estimator in the context of these problems we compute global effectivity indices and utilize the local element wise effectivity index in computing three additional measures the first of these is the robustness index the others are the modified robustness index and the distribution index which are introduced for the first time it is found that the global effectivity index varies with problem parameters in particular the wave number robustness indices also vary due to the local error definition and wave number values of the distribution index are much better however indicating the suitability of the error estimator in guiding efficient adaptive mesh refinement the analysis of the error estimator is carried out on relatively coarse meshes typical of those used in practical engineering computations

solving boundary value problems integral and integro differential equations using gegenbauer integration matrices we introduce a hybrid gegenbauer ultraspherical integration method hgim for solving boundary value problems bvps integral and integro differential equations the proposed approach recasts the original problems into their integral formulations which are then discretized into linear systems of algebraic equations using gegenbauer integration matrices gims the resulting linear systems are well conditioned and can be easily solved using standard linear system solvers a study on the error bounds of the proposed method is presented and the spectral convergence is proven for two point bvps tpbvps comparisons with other competitive methods in the recent literature are included the proposed method results in an efficient algorithm and spectral accuracy is verified using eight test examples addressing the aforementioned classes of problems the proposed method can be applied on a broad range of mathematical problems while producing highly accurate results the developed numerical scheme provides a viable alternative to other solution methods when high order approximations are required using only a relatively small number of solution nodes

a time space flux corrected transport finite element formulation for solving multi dimensional advection diffusion reaction equations abstract we present a time space flux corrected transport fct finite element formulation for the multi dimensional time dependent advection diffusion reaction equation monotonic solutions can be achieved with the presented method while large time steps with courant number c r 1 are used numerical verification as well as a grid convergence analysis are carried out for 1d and 2d benchmark problems a 1d burgers equation with various reynolds numbers is solved with the time space fct method in addition a 2d transport problem with and without a nonlinear reaction inside of a cavity is considered finally the newly developed time space fct formulation is applied for modeling biofilm growth problems based on a continuum mathematical model it turns out that the time space fct method helps to reduce numerical dissipation and guarantees comparable numerical dispersion of the solution at the same time comparing to numerical solutions obtained by a time space finite incremental calculus fic method

a symmetric formulation for computing transient shallow water flows abstract the shallow water equations fall into the category of symmetric advective diffusive systems with source terms these types of equations can be very effectively solved using stabilized methods such as supg and gls a semi discrete finite element method based on these ingredients is presented for the computation of transient shallow water flows special care has been taken in the design of the operators in order to improve the performance for unsteady calculations the solution is advanced in time via a predictor multi corrector algorithm which includes as special cases the second order trapezoidal rule a first order explicit method and a first order implicit method equivalent to the constant in time element of the space time formulation

towards the resolution of the gibbs phenomena it is well known that the expansion of an analytic nonperiodic function on a finite interval in a fourier series leads to spurious oscillations at the interval boundaries this result is known as the gibbs phenomenon the present paper introduces a new method for the resolution of the gibbs phenomenon which follows on the reconstruction method of gottlieb and coworkers siam rev 39 1997 644 based on gegenbauer polynomials orthogonal with respect to weight function 1 x2 1 2 we refer to their approach as the direct method and to the new methodology as the inverse method both methods use the finite set of fourier coefficients of some given function as input data in the re expansion of the function in gegenbauer polynomials or in other orthogonal basis sets the finite partial sum of the new expansion provides a spectrally accurate approximation to the function in the direct method this requires that certain conditions are met concerning the parameter in the weight function the number of fourier coefficients n and the number of gegenbauer polynomials m we show that the new inverse method can give exact results for polynomials independent of and with m n the paper presents several numerical examples applied to a single domain or to subdomains of the main domain so as to illustrate the superiority of the inverse method in comparison with the direct method

on stabilized finite element methods for linear systems of convection diffusion reaction equations abstract a stabilized finite element method for solving systems of convection diffusion reaction equations is studied in this paper the method is based on the subgrid scale approach and an algebraic approximation to the subscales after presenting the formulation of the method it is analyzed how it behaves under changes of variables showing that it relies on the law of change of the matrix of stabilization parameters associated to the method an expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a one dimensional 1d model problem applications of the stabilization technique to the stokes problem with convection and to the bending of reissner mindlin plates are discussed next the design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard galerkin method applied to these two problems

on the gibbs phenomenon i recovering exponential accuracy from the fourier partial sum of a nonperiodic analytic function it is well known that the fourier series of an analytic and periodic function truncated after 2n 1 terms converges exponentially with n even in the maximum norm it is also known that if the function is not periodic the rate of convergence deteriorates in particular there is no convergence in the maximum norm although the function is still analytic this is known as the gibbs phenomenon in this paper we show that the first 2n 1 fourier coefficients contain enough information about the function so that an exponentially convergent approximation in the maximum norm can be constructed the proof is a constructive one and makes use of the gegenbauer polynomials c n x it consists of two steps in the first step we show that the first m coefficients of the gegenbauer expansion based on c n x for 0 n m of any l2 function can be obtained within exponential accuracy provided that both and m are proportional to but smaller than n in the second step we construct the gegenbauer expansion based on c n 0 n m from the coefficients found in the first step we show that this series converges exponentially with n provided that the original function is analytic though nonperiodic thus we prove that the gibbs phenomenon can be completely overcome

enforcement of constraints and maximum principles in the variational multiscale method abstract we present a new theoretical framework for the enforcement of constraints in variational multiscale vms analysis the theory is first presented in an abstract operator format and subsequently specialized for the steady advection diffusion equation the approach borrows heavily from results in constrained and convex optimization an exact expression for the fine scales is derived in terms of variational derivatives of the constraints lagrange multipliers and a fine scale green s function the methodology described enables the development of numerical methods which satisfy predefined attributes a practical and effective procedure for solving the steady advection diffusion equation is presented based on a vms inspired stabilized method weakly enforced dirichlet boundary conditions and enforcement of a maximum principle and conservation constraint

estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the helmholtz equation an estimator for the error in the wave number is presented in the context of finite element approximations of the helmholtz equation the proposed estimate is an extension of the ideas introduced in steffens and d iez comput methods appl mech engng 2009 198 1389 1400 in the previous work the error assessment technique was developed for standard galerkin approximations here the methodology is extended to deal also with stabilized approximations of the helmholtz equation thus the accuracy of the stabilized solutions is analyzed including also their sensitivity to the stabilization parameters depending on the mesh topology the procedure builds up an inexpensive approximation of the exact solution using post processing techniques standard in error estimation analysis from which the estimate of the error in the wave number is computed using a simple closed expression the recovery technique used in steffens and diez comput methods appl mech engng 2009 198 1389 1400 is based in a polynomial least squares fitting here a new recovery strategy is introduced using exponential in a complex setup trigonometric local approximations respecting the nature of the solution of the wave problem copyright 2011 john wiley sons ltd

a modified streamline diffusion method for solving the stationary navier stokes equation recently hughes et al 11 12 proposed new finite element schemes of petrov galerkin type for solving the stokes problem which do not require the discrete version of the ladyshenskaya babuska brezzi condition lbb condition in this paper we derive a conforming finite element method for solving the stationary navier stokes equations which combines the advantages of arbitrary finite element spaces for velocity pressure with the favourable properties of the streamline diffusion method in the case of moderate and high reynolds number

a stabilized finite element method for the incompressible magnetohydrodynamic equations we propose and analyze a stabilized finite element method for the incompressible magnetohydrodynamic equations the numerical results that we present show a good behavior of our approximation in experiments which are relevant from an industrial viewpoint we explain in particular in the proof of our convergence theorem why it may be interesting to stabilize the magnetic equation as soon as the hydrodynamic diffusion is small and even if the magnetic diffusion is large this observation is confirmed by our numerical tests

a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

relative quantification based on logistic models for individual polymerase chain reactions the quantitative real time reverse transcription polymerase chain reaction rt pcr technology measures molecular variations in specific biomarkers relative quantification determines the target expression relative to an external standard or reference sample and should be adjusted for the pcr efficiencies actually achieved more accurate methods of estimating pcr efficiency require a number of serial dilutions of the target sample which is not generally feasible for clinical specimens alternatively the efficiency of a single reaction may be estimated by considering kinetic data from this reaction the current methods of estimating individual reaction efficiency require finding its exponential phase which may affect the accuracy and precision of efficiency estimates thus a model adequately representing all available kinetic rt pcr data is preferable but no such model is currently in use for relative quantification in this work we use a logistic model for all kinetic data from each rt pcr and propose a new method of efficiency adjusted relative quantification based on the estimates from the fitted logistic models this method allows incorporating multiple replicates and possibly multiple reference housekeeping genes for estimating relative expression and corresponding confidence interval real kinetic rt pcr data are used to compare the proposed and standard methods the methods are applied to the clinical data from the ongoing study of guanylyl cyclase c as a biomarker for colorectal cancer

eigenvalue bounds for the schur complement with a pressure convection diffusion preconditioner in incompressible flow computations if the stationary navier stokes system or an implicit time discretization of the evolutionary navier stokes system is linearized by a picard iteration and discretized in space by a mixed finite element method there arises a saddle point system which may be solved by a krylov subspace method or an uzawa type approach for each of these resolution methods it is necessary to precondition the schur complement associated to the saddle point problem in question in the work at hand we give upper and lower bounds of the eigenvalues of this schur complement under the assumption that it is preconditioned by a pressure convection diffusion matrix

a least squares petrov galerkin finite element method for the stationary navier stokes equations in this paper a galerkin least squares type finite element method is proposed and analyzed for the stationary navier stokes equations the method is consistent and stable for any combination of discrete velocity and pressure spaces without requiring a babuska brezzi stability condition the existence uniqueness and convergence at optimal rate of the discrete solution is proved in the case of sufficient viscosity or small data

k version of finite element method in gas dynamics higher order global differentiability numerical solutions in this paper we consider and examine alternate finite element computational strategies for time dependent navier stokes equations describing high speed compressible flows with shocks in a viscous and conducting medium with the ultimate objective of establishing the desired features of a general mathematical and computational framework for such initial value problems ivp in which a the numerically computed solutions are in agreement with the physics of evolution described by the governing differential equations gdes i e the ivp b the solutions are admissible in the non discretized form of the gdes in the pointwise sense i e anywhere and everywhere in the entire space time domain and hence in the integrated sense as well c the numerical approximations progressively approach the same global differentiability in space and time as the theoretical solutions d it is possible to time march the solutions this is essential for efficiency as well as ensuring desired accuracy of the computed solution for the current increment of time i e to minimize the error build up in the time marching process e the computational process is unconditionally stable and non degenerate regardless of the choice of discretization nature of approximations and their global differentiability and the dimensionless parameters influencing the physics of the process f there are no issues of stability cfl number limitations and g the mathematical and computational methodology is independent of the nature of the space time differential operators we consider one dimensional compressible flow in a viscous and conducting medium with shocks as model problems to illustrate various features of the general mathematical and computational framework used here and to demonstrate that the proposed framework is general and is applicable to all ivp the riemann shock tube with a single diaphragm serves as a model problem the specific details presented in the paper discuss 1 choice of the form of the gdes i e strong form or weak form 2 various choices of variables the paper establishes and considers density velocity and temperature as variables of choice 3 details of the space time least squares ls integral forms meritorious over all others in all aspects are presented and choice of approximation spaces are discussed 4 in all numerical studies we consider a viscous and conducting medium with ideal gas law however results are also presented for non conducting medium extension of this work to real gas models will be presented in a separate paper it is worth noting that when the medium is viscous and conducting the solutions of gas dynamics equations are analytic 5 it is also significant to note that upwinding methods based on addition of artificial diffusion such as supg supg dc supg dc ls and their many variations are neither needed nor used in this present work 6 numerical studies are aimed at resolving the localized details of the shock structure i e shock relations shock width shock speed etc as well as the over all global behaviour of the solution in the entire space time domain 7 numerical studies are presented for riemann shock tube for high mach number flows with special emphasis also on time accuracy of the evolution which is ensured by requiring that the approximations for each increment of time satisfy non discretized form of the gdes in the pointwise sense and hence in the integrated sense as well 8 comparisons are made with published results as well as theoretical solutions when possible it is established that space time least squares processes are the only processes that yield variationally consistent space time integral forms and hence unconditionally non degenerate space time computational processes which when considered in higher order scalar product spaces provide the desired mathematical framework in which progressively higher order global differentiability solutions in space and time yield the same characteristics as the theoretical solutions of the ivp in all aspects copyright 2006 john wiley sons ltd

stabilized mixed finite element formulations for materially nonlinear partially saturated two phase media standard and enhanced bbar or eas low order finite elements applied to the problem of consolidation of two phase nonlinear continua do not satisfy the lbb condition when the same interpolation functions are used for both displacement and pore pressure fields strong spatial pressure oscillations are the main consequence of the lbb condition violation the class of direct stabilized methods widely used in the field of fluid mechanics is a powerful tool to circumvent violation of the aforementioned condition three stabilized formulations designed for the problem of consolidation of fully or partially saturated media are presented galerkin least squares gls with the least squares term construction based on the residuum of the local fluid mass conservation equation the pressure stabilized formulation fpl in which the rate of the pore pressure laplacian residual free in the incompressibility limit is added to the fluid mass conservation equation and finally a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation an h convergence study and test problems for the three stabilized schemes are discussed

the equivalence of weak strong and complete convergence in l_1 for kernel density estimates theorem 1 let k be a nonnegative borel measurable function on rd with f k x dx 1 then the following conditions are equivalent i j 0 in probability as n oo some f ii jn o 0 in probability as n s oo all f iii jn s 0 almost surely as n oo all f iv jn 0 exponentially as n oc i e for all e 0 there exist r no 0 such that p jne no all f v lim0h 0 and limnnhd oo also v implies iv when k is merely absolutely integrable and f k x dx 1 0

a least squares galerkin petrov nonconforming mixed finite element method for the stationary conduction convection problem abstract in this paper a least squares galerkin petrov nonconforming mixed finite element method lsgpnmfm is proposed and analyzed for the stationary conduction convection problem we use p 2 nonconforming as approximation space for the velocity the linear element for the pressure space and the quadratic element for the temperature space the mixed finite element spaces x h and m h need not satisfy inf sup condition the existence uniqueness and convergence of the discrete solution are presented and error estimates of optimal order are derived in the case of sufficient viscosity

stabilized finite element method for viscoplastic flow formulation and a simple progressive solution strategy abstract this paper presents a stabilized finite element formulation for steady state viscoplastic flow and a simple strategy for solving the resulting non linear equations with a newton raphson algorithm an eulerian stabilized finite element formulation is presented where mesh dependent terms are added element wise to enhance the stability of the mixed finite element formulation a local reconstruction method is used for computing derivatives of the stress field needed when higher order elements are used linearization of the weak form is derived to enable a newton raphson solution procedure of the resulting non linear equations in order to get convergence in the newton raphson algorithm a trial solution is needed which is within the radius of convergence an effective strategy for progressively moving inside the radius of convergence for highly non linear viscoplastic constitutive equations typical of metals is presented numerical experiments using the stabilization method with both linear and quadratic shape functions for the velocity and pressure fields in viscoplastic flow problems show that the stabilized method and the progressive convergence strategy are effective in non linear steady forming problems finally conclusions are inferred and extensions of this work are discussed

analysis of a discontinuous galerkin method for the biot s consolidation problem in this paper a fully discrete stabilized discontinuous galerkin method is proposed to solve the biot s consolidation problem the existence and uniqueness of the finite element solution are obtained the stability of the fully discrete solution is discussed the corresponding error estimates for the approximation of displacement and pressure in a mesh dependent norm are obtained the error estimate for the approximation of pressure in l 2 norm is also obtained

a numerical method for large eddy simulation in complex geometries we discuss the development of a numerical algorithm and solver capable of performing large eddy simulation in the very complex geometries often encountered in industrial applications the algorithm is developed for unstructured hybrid grids is non dissipative yet robust at high reynolds numbers on highly skewed grids simulation results for a variety of flows are presented

the space continuous discontinuous galerkin method abstract the space discontinuous finite element method for a scalar diffusion convection reaction problem is introduced and analyzed in the solution method the boundary conditions and the continuity of the solution at the element interfaces are forced in a weak sense the convergence rate of the numerical solution is shown however to be the same as in the usual approach based on a continuous approximation finally the benefits of the method with discontinuous continuous approximation in h adaptation of the finite element space are illustrated with the aid of numerical calculations

stability of semidiscrete formulations for parabolic problems at small time steps solutions of direct time integration schemes that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations along with attendant overshoot in time this degradation is not an artifact of the time marching scheme but rather a property of the solution of the semidiscrete formulation itself a critical time step for the onset of spatial oscillations is derived by analogy to singularly perturbed elliptic problems we then propose a simple procedure of spatial stabilization to remove this pathology from implicit time integration schemes without affecting unconditional temporal stability spatially stabilized implicit time integration is free of spurious spatial oscillations at small time steps and numerical experience points to improved temporal accuracy as well

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

a novel least squares finite element method enriched with residual free bubbles for solving convection dominated problems in this paper we devise a novel least squares finite element method lsfem for solving scalar convection dominated convection diffusion problems first we convert a second order convection diffusion problem into a first order system formulation by introducing the gradient mathbf p kappa nabla u as an additional variable the lsfem using continuous piecewise linear elements enriched with residual free bubbles for both variables u and mathbf p is applied to solve the first order mixed problem the residual free bubble functions are assumed to strongly satisfy the associated homogeneous second order convection diffusion equations in the interior of each element up to the contribution of the linear part and vanish on the element boundary to implement this two level least squares approach a stabilized method of galerkin least squares type is used to approximate the residual free bubble functions this enriched lsfem not only inherits the advantages of the primitive lsfem such as the resulting linear system being symmetric and positive definite but also exhibits the characteristics of the residual free bubble method without involving stability parameters several numerical experiments are given to demonstrate the effectiveness of the proposed enriched lsfem the accuracy and computational cost of this enriched lsfem are also compared with those of the primitive lsfem we find that for a small diffusivity kappa the enriched lsfem is much better able to capture the nature of layer structure in the solution than the primitive lsfem even if the primitive lsfem uses a very fine mesh or higher order elements in other words the enriched lsfem provides a significant improvement with a lower computational cost over the primitive lsfem for solving convection dominated problems

heteroscedastic nonlinear regression several parameter estimation methods for dealing with heteroscedasticity in nonlinear regression are described these include variations on ordinary weighted iteratively reweighted extended and generalized least squares some of these variations are new and one of them in particular modified extended iteratively reweighted least squares meirls allows parameters of an assumed heteroscedastic variance model to be estimated with an adjustment for bias due to estimation of the regression parameters the context of the discussion is primarily that of pharmacokinetic type data although an example is given involving chemical reaction data using simulated data from 21 heteroscedastic pharmacokinetic type models some of the methods are compared in terms of mean absolute error and 95 confidence interval coverage from these comparisons meirls and the variations on generalized least squares emerge as the methods of choice

stabilized reduced basis methods for parametrized steady stokes and navier stokes equations abstract it is well known in the reduced basis approximation of saddle point problems that the galerkin projection on the reduced space does not guarantee the inf sup approximation stability even if a stable high fidelity method was used to generate snapshots for problems in computational fluid dynamics the lack of inf sup stability is reflected by the inability to accurately approximate the pressure field in this context inf sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions the main goal of this work is to propose an alternative approach which relies on the residual based stabilization techniques customarily employed in the finite element literature such as brezzi pitkaranta franca hughes streamline upwind petrov galerkin galerkin least square in the spirit of offline online reduced basis computational splitting two such options are proposed namely offline only stabilization and offline online stabilization these approaches are then compared to and combined with the state of the art supremizer enrichment approach numerical results are discussed highlighting that the proposed methodology allows to obtain smaller reduced basis spaces i e neglecting supremizer enrichment for which a modified inf sup stability is still preserved at the reduced order level

a finite element formulation of compressible flows using various sets of independent variables abstract this paper presents a finite element method for the simulation of compressible flows the navier stokes and euler equations are solved in the conservation form using various sets of independent variables a variational formulation is developed based upon a variant of the petrov galerkin method and uses a shock capturing operator an adaptive algorithm based on a particular residual norm is proposed several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high speed flows

a new projection based stabilized method for steady convection dominated convection diffusion equations abstract we propose a new projection based stabilized method for the steady convection dominated convection diffusion equations this method directly increases the l 2 stability instead of the h 1 stability which the variational multiscale vms methods do numerical analysis and numerical experiments illustrate and confirm that our new method has effective numerical performances on convection dominated convection diffusion problems

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

a general approach for two stage analysis of multilevel clustered non gaussian data in this article we propose a two stage approach to modeling multilevel clustered non gaussian data with sufficiently large numbers of continuous measures per cluster such data are common in biological and medical studies utilizing monitoring or image processing equipment we consider a general class of hierarchical models that generalizes the model in the global two stage gts method for nonlinear mixed effects models by using any square root n consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model and by extending the stage 2 model to accommodate random effects from multiple levels of clustering the second stage model is a standard linear mixed effects model with normal random effects but the cluster specific distributions conditional on random effects can be non gaussian this methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest for estimation of the population parameters we propose a conditional restricted maximum likelihood creml approach and establish the asymptotic properties of the creml estimators the proposed general approach is illustrated using quartiles as cluster specific parameters estimated in the first stage and applied to the data example from a collagen fibril development study we demonstrate using simulations that in samples with small numbers of independent clusters the creml estimators may perform better than conditional maximum likelihood estimators which are a direct extension of the estimators from the gts method

on the gibbs phenomenon and its resolution the nonuniform convergence of the fourier series for discontinuous functions and in particular the oscillatory behavior of the finite sum was already analyzed by wilbraham in 1848 this was later named the gibbs phenomenon this article is a review of the gibbs phenomenon from a different perspective the gibbs phenomenon as we view it deals with the issue of recovering point values of a function from its expansion coefficients alternatively it can be viewed as the possibility of the recovery of local information from global information the main theme here is not the structure of the gibbs oscillations but the understanding and resolution of the phenomenon in a general setting the purpose of this article is to review the gibbs phenomenon and to show that the knowledge of the expansion coefficients is sufficient for obtaining the point values of a piecewise smooth function with the same order of accuracy as in the smooth case this is done by using the finite expansion series to construct a different rapidly convergent approximation

a variational multiscale method based on bubble functions for convection dominated convection diffusion equation this work presents a variational multiscale method based on polynomial bubble functions as subgrid scale and a numerical implementation based on two local gauss integrations this method can be implemented easily and efficiently for the convection dominated problem static condensation of the bubbles suggests the stability of the method and we establish its global convergence representative numerical tests are presented

an arbitrary lagrangian eulerian finite element method for solving three dimensional free surface flows abstract this paper discusses numerical solution of unsteady three dimensional free surface flows the governing equilibrium equations are written in the framework of the arbitrary lagrangian eulerian kinematic description the corresponding variational formulation is established afterwards since the variational problems are nonlinear with respect to the moving coordinates a second order approximate variational problem is derived after a consistent linearization of the referential motion stability of the discrete formulations is ensured with the help of a new stabilization method a robust preconditioned gmres algorithm is then used to solve the resulting set of nonlinear equations finally the computational algorithms are assessed through numerical studies of various problems a large sloshing flow in a three dimensional reservoir a discharge flow from a reservoir simulation of a liquid vortex produced inside a cylindrical container with a disk rotating at the bottom and a three dimensional practical hydraulic problem

an anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

a new absolutely stable simplified galerkin least squares finite element method using nonconforming element for the stokes problem we propose a new absolutely stable simplified galerkin least squares sgls finite element method using equal order linear nonconforming element for the stokes problem we prove that our method is absolutely stable and has optimal error estimates numerical tests confirm and illustrate the theoretical analysis compare with the conforming galerkin least squares method and conforming sgls method our nonconforming method is more accuracy

a cbs type stabilizing algorithm for the consolidation of saturated porous media the presented method stems from the works by zienkiewicz and co workers for coupled fluid thermal problems starting from the early 1990s they propose algorithms to overcome the difficulties connected to the application of the fem to the area of fluid mechanics which include the problems of singular behaviour in incompressibility and the problems connected to convective terms the major step forward was to introduce the concept of characteristic lines the particle paths in a simple convection situation for a class of problems with a single scalar variable the equations in the characteristic co ordinates regain self adjointness the procedure is called characteristic based split algorithm cbs we use here a cbs type procedure for a saturated deformable elastic porous medium in which the fluid velocity is governed by darcy s equation which comes directly from navier stokes ones the physical mathematical model is a fully coupled one and is here used to study an incompressible flow inside a continuum with incompressible solid grains the power of the adopted algorithm is to treat the basic equations in their strong form and to transform a usual u p problem into a u v p one where u generally indicates the displacement of the solid matrix and p and v the pressure and velocity of the fluid respectively attention is focused on the expression of darcy s velocity which is considered as the starting point of the algorithm the accuracy of the scheme is checked by comparing the present predictions in a typical consolidation test with available analytical and numerical u p solutions a good fitting among different results has been obtained it is further shown that the procedure eliminates the oscillations at the onset of consolidation typical for many schemes the fem code ed multifield has been used for implementing and testing the procedure copyright 2005 john wiley sons ltd

efficient inference for random coefficient growth curve models with unbalanced data growth and dose response curve studies often result in incomplete or unbalanced data random effects models together with a variety of computer intensive iterative techniques have been suggested for the analysis of such data this paper is concerned with a noniterative method for estimating and comparing location parameters in random coefficient growth curve models consistent and asymptotically efficient estimators of the location parameters are obtained using estimated generalized least squares two criteria for testing multivariate general linear hypotheses are introduced and their asymptotic properties are investigated the results are applied to clinical data obtained on the blood ultrafiltration performance of hemodialyzers used in the treatment of patients with end stage renal disease

cfd shape optimization using an incomplete gradient adjoint formulation a design methodology based on the adjoint approach for flow problems governed by the incompressible euler equations is presented the main feature of the algorithm is that it avoids solving the adjoint equations which saves an important amount of cpu time furthermore the methodology is general in the sense it does not depend on the geometry representation all the grid points on the surface to be optimized can be chosen as design parameters in addition the methodology can be applied to any type of mesh the partial derivatives of the flow equations with respect to the design parameters are computed by finite differences in this way this computation is independent of the numerical scheme employed to obtain the flow solution once the design parameters have been updated the new solid surface is obtained with a pseudo shell approach in such a way that local singularities which can degrade or inhibit the convergence to the optimal solution are avoided some 2d and 3d numerical examples are shown to demonstrate the proposed methodology copyright 2001 john wiley sons ltd

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented

adaptive spacetime discontinuous galerkin method for hyperbolic advection diffusion with a non negativity constraint summary applications where the diffusive and advective time scales are of similar order give rise to advection diffusion phenomena that are inconsistent with the predictions of parabolic fickian diffusion models non fickian diffusion relations can capture these phenomena and remedy the paradox of infinite propagation speeds in fickian models in this work we implement a modified frame invariant form of cattaneo s hyperbolic diffusion relation within a spacetime discontinuous galerkin advection diffusion model an h adaptive spacetime meshing procedure supports an asynchronous patch by patch solution procedure with linear computational complexity in the number of spacetime elements this localized solver enables the selective application of optimization algorithms in only those patches that require inequality constraints to ensure a non negative concentration solution in contrast to some previous methods we do not modify the numerical fluxes to enforce non negative concentrations thus the element wise conservation properties that are intrinsic to discontinuous galerkin models are defined with respect to physically meaningful riemann fluxes on the element boundaries we present numerical examples that demonstrate the effectiveness of the proposed model and we explore the distinct features of hyperbolic advection diffusion response in subcritical and supercritical flows copyright 2015 john wiley sons ltd

analysis and application of fourier gegenbauer method to stiff differential equations the fourier gegenbauer fg method introduced by gottlieb shu solomonoff and vandeven icase report 92 4 hampton va 1992 is aimed at removing the gibbs phenomenon that is recovering the point values of a nonperiodic function from its fourier coefficients in this paper we discuss some numerical aspects of the fg method related to its em pseudospectral implementation in particular we analyze the behavior of the gegenbauer series with a moderate several hundred number of terms suitable for computations we also demonstrate the ability of the fg method to get a spectrally accurate approximation on small subintervals for rapidly oscillating functions or functions having steep profiles bearing on the previous analysis we suggest a high order spectral fourier method for the solution of nonperiodic differential equations it includes a polynomial subtraction technique to accelerate the convergence of the fourier series and the fg algorithm to evaluate derivatives on the boundaries of nonperiodic functions the present hybrid fourier gegenbauer hfg method possesses better resolution properties than the original fg method the precision of this method is demonstrated by solving stiff elliptic problems with steep solutions

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

a space time coupled p version least squares finite element formulation for unsteady fluid dynamics problems this paper presents a p version least squares finite element formulation for unsteady fluid dynamics problems where the effects of space and time are coupled the dimensionless form of the differential equations describing the problem are first cast into a set of first order differential equations by introducing auxiliary variables this permits the use of c element approximation the element properties are derived by utilizing p version approximation functions in both space and time and then minimizing the error functional given by the space time integral of the sum of squares of the errors resulting from the set of first order differential equations this results in a true space time coupled least squares minimization procedure a time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step the space time coupled p version approximation functions provide the ability to control truncation error which in turn permits very large time steps what literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space time coupled approach for non linear problems the non linear algebraic equations resulting from the least squares process are solved using newton s method with a line search this procedure results in a symmetric hessian matrix equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance the generality success and superiority of the present formulation procedure is demonstrated by presenting specific formulations and examples for the advection diffusion and burgers equations the results are compared with the analytical solutions and those reported in the literature the formulation presented here is ideally suited for space time adaptive procedures the element error functional values provide a mechanism for adaptive h p or hp refinements the work presented in this paper provides the basis for the extension of the space time coupled least squares minimization concept to two and three dimensional unsteady fluid flow

some simple methods for estimating intraindividual variability in nonlinear mixed effects models methods are proposed to improve both population and individual inference within the nonlinear random coefficient regression framework by incorporating possible heterogeneity in the intraindividual variance structure these methods extend existing variance function estimation techniques by pooling information across individuals the methods are appropriate when it is reasonable to assume that there exists a common intraindividual variance structure

local projection stabilized method on unsteady navier stokes equations with high reynolds number using equal order interpolation in this paper we propose and analyze a stabilized method for unsteady navier stokes equations with high reynolds number using local projection stabilized method to control spurious oscillations in the velocities due to dominant convection or in the pressure due to the velocity pressure coupling using equal order conforming elements in space and crank nicolson difference in time we derive a fully discrete formulation we prove stability and convergence of the approximate solution the error estimates hold irrespective of the reynolds number provided the exact solution is smooth this result is comparable with the streamline diffusion and continuous interior penalty methods

a new family of stable elements for nearly incompressible elasticity based on a mixed petrov galerkin finite element formulation adding to the classical hellinger reissner formulation another residual form of the equilibrium equation a new petrov galerkin finite element method is derived it fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations including equal order discontinuous stress and continuous displacement interpolations which are unstable within the galerkin approach error estimates are presented using the babuska brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method

a hybrid fast multipole pseudo spectral time domain method the major computation cost of pseudo spectral method comes from the evaluation of differentiation matrix multiplication in the past uniform or chebyshev collocation points are used for sampling the differentiation matrix multiplication was evaluated by fast fourier transform fft or fast cosine transform fct in order to reduce the computation complexity from o n2 to o n log n however the intrinsic properties of fft or fct may cause the wraparound effect and gibbs phenomenon moreover fft or fct is not applicable to other collocation points such as legendre and hermite in order to improve the accuracy and applicability of the pseudo spectral method the fast multipole method fmm is exploited to substitute the fft or fct by making use of the similarity of the n body problem and the collocation problem a new fmm based pseudo spectral time domain method is developed in this paper

analysis of the small viscosity and large reaction coefficient in the computation of the generalized stokes problem by a novel stabilized finite element method abstract in this paper we propose and analyze a novel stabilized finite element method fem for the system of generalized stokes equations arising from the time discretization of transient stokes problem the system involves a small viscosity which is proportional to the inverse of large reynolds number and a large reaction coefficient which is the inverse of small time step the proposed stabilized fem employs the c 0 piecewise linear elements for both velocity field and pressure on the same mesh and uses the residuals of the momentum equation and the divergence free equation to define the stabilization terms the stabilization parameters are fixed and element independent without a comparison of the viscosity the reaction coefficient and the mesh size using the finite element solution of an auxiliary boundary value problem as the interpolating function for velocity and the h 1 seminorm projection for pressure instead of the usual nodal interpolants we derive error estimates for the stabilized finite element approximations to velocity and pressure in the l 2 and h 1 norms and most importantly we explicitly establish the dependence of error bounds on the viscosity the reaction coefficient and the mesh size our analysis reveals that this stabilized fem is particularly suitable for the generalized stokes system with a small viscosity and a large reaction coefficient which has never been achieved before in the error analysis of other stabilization methods in the literature we then numerically confirm the effectiveness of the proposed stabilized fem comparisons made with other existing stabilization methods show that the newly proposed method can attain better accuracy and stability

new substructuring domain decomposition methods for advection diffusion equations abstract in this paper we consider a nonsymmetric elliptic problem and we use the techniques related to the steklov poincare operators to propose new substructuring iterative procedures in particular we propose two methods that generalize the well known neumann neumann and dirichlet neumann iterative procedures we prove that our methods that use symmetric and positive definite preconditioners lead to the construction of iterative schemes with optimal convergence properties numerical results for the finite element discretization are given

a fic based stabilized finite element formulation for turbulent flows abstract we present a new stabilized finite element fem formulation for incompressible flows based on the finite increment calculus fic framework onate 1998 in comparison to existing fic approaches for fluids this formulation involves a new term in the momentum equation which introduces non isotropic dissipation in the direction of velocity gradients we also follow a new approach to the derivation of the stabilized mass equation inspired by recent developments for quasi incompressible flows onate et al 2014 the presented fic fem formulation is used to simulate turbulent flows using the dissipation introduced by the method to account for turbulent dissipation in the style of implicit large eddy simulation

modeling of steep layers in singularly perturbed diffusion reaction equation via flexible fine scale basis abstract we present a new stabilized method for the diffusion reaction equation which develops sharp boundary and or internal layers for the reaction dominated case i e singularly perturbed case the method relies on an improved expression for the stabilization parameter that is derived via the fine scale variational formulation facilitated by the variational multiscale vms framework the proposed fine scale basis consists of enrichment functions which may be nonzero at element edges the derived stabilization parameter enjoys spatial variation over element interiors and along inter element boundaries that helps model the rapid variation of the residual of the euler lagrange equations over the domain this feature also facilitates consistent stabilization across boundary and internal layers as well as capturing anisotropic refinement effects the method is able to better satisfy the maximum principle as compared to other existing methods we present a priori mathematical analysis of the stability and convergence of the method for the diffusion reaction equation optimal convergence on meshes comprised of linear triangles and bilinear quadrilateral elements are presented for smooth problems as well as for problems with steep boundary layers stability and accuracy features of the method for problems with discontinuous forcing function internal layers and boundary layers are shown and its performance on unstructured and distorted meshes comprised of quadrilateral and triangular elements is highlighted

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

determining analyticity for parameter optimization of the gegenbauer reconstruction method the gegenbauer reconstruction method effectively eliminates the gibbs phenomenon and restores exponential accuracy to the approximations of piecewise smooth functions recent investigations show that its success depends upon choosing parameters in such a way that the regularization and the truncation error estimates are equally considered this paper shows that the underlying analyticity of the function in smooth regions plays a critical role in the regularization error estimate hence we develop a technique that first analyzes the behavior of the function in its regions of smoothness and then applies this knowledge to refine the regularization error estimate such refinement yields better parameter choices for the gegenbauer reconstruction method and is confirmed both by better accuracy and more robustness in the approximation of piecewise smooth functions

on upwind methods for parabolic finite elements in incompressible flows we study the performance of various upwind techniques implemented in parabolic finite element discretizations for incompressible high reynolds number flow the characteristics of an ideal upwind procedure are first discussed then the streamline upwind petrov galerkin method a simplified version thereof the galerkin least squares technique and a high order derivative artificial diffusion method are evaluated on test problems we conclude that none of the methods displays the desired solution characteristics there is still need for the development of a reliable and efficient upwind method with characteristics close to those of the ideal procedure copyright 2000 john wiley sons ltd

an adaptive stabilized conforming finite element method via residual minimization on dual discontinuous galerkin norms abstract we design and analyze a new adaptive stabilized finite element method we construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that has inf sup stability we formulate this residual minimization as a stable saddle point problem which delivers a stabilized discrete solution and a residual representation that drives the adaptive mesh refinement numerical results on an advection reaction model problem show competitive error reduction rates when compared to discontinuous galerkin methods on uniformly refined meshes and smooth solutions moreover the technique leads to optimal decay rates for adaptive mesh refinement and solutions having sharp layers

a stabilized nonconfirming finite element method based on multiscale enrichment for the stationary navier stokes equations abstract in the paper we proposed a stabilized nonconforming finite element method for the stationary incompressible navier stokes equations which is a petrov galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions and we studied the stability of the method for p 1 p 0 triangular element q 1 p 0 quadrilateral element and obtained the optimal error estimates of the stabilized nonconforming finite element method for the stationary navier stokes equations

on the roles of minimization and linearization in least squares finite element models of nonlinear boundary value problems in this paper we examine the roles of minimization and linearization in the least squares finite element formulations of nonlinear boundary values problems the least squares principle is based upon the minimization of the least squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations in the present case we consider l 2 norms since the least squares method is independent of the discretization procedure and the solution scheme the least squares principle suggests that minimization should be performed prior to linearization where linearization is employed in the context of either the picard or newton iterative solution procedures however in the least squares finite element analysis of nonlinear boundary value problems it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations the main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged the assessment is performed mathematically through an examination of the variational setting for the least squares formulation of an abstract nonlinear boundary value problem and also computationally through the numerical simulation of the least squares finite element solutions of both a nonlinear form of the poisson equation and also the incompressible navier stokes equations the assessment suggests that although the least squares principle indicates that minimization should be performed prior to linearization such an approach is often impractical and not necessary

a bayesian approach to nonlinear random effects models nonlinear random effects models are considered from the bayesian point of view the method of analysis follows closely that of lindley and smith 1972 journal of the royal statistical society series b 34 1 42 the numerical method is related to the em algorithm

a bubble stabilized least squares finite element method for steady mhd duct flow problems at high hartmann numbers in this paper we devise a stabilized least squares finite element method using the residual free bubbles for solving the governing equations of steady magnetohydrodynamic duct flow we convert the original system of second order partial differential equations into a first order system formulation by introducing two additional variables then the least squares finite element method using c 0 linear elements enriched with the residual free bubble functions for all unknowns is applied to obtain approximations to the first order system the most advantageous features of this approach are that the resulting linear system is symmetric and positive definite and it is capable of resolving high gradients near the layer regions without refining the mesh thus this approach is possible to obtain approximations consistent with the physical configuration of the problem even for high values of the hartmann number before incoorperating the bubble functions into the global problem we apply the galerkin least squares method to approximate the bubble functions that are exact solutions of the corresponding local problems on elements therefore we indeed introduce a two level finite element method consisting of a mesh for discretization and a submesh for approximating the computations of the residual free bubble functions numerical results confirming theoretical findings are presented for several examples including the shercliff problem

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

trouble with gegenbauer reconstruction for defeating gibbs phenomenon runge phenomenon in the diagonal limit of gegenbauer polynomial approximations to defeat gibbs phenomenon in fourier and chebyshev series gottlieb et al d gottlieb c w shu a solomonoff h vandeven on the gibbs phenomenon i recovering exponential accuracy from the fourier partial sum of a nonperiodic analytic function j comput appl math 43 1992 81 98 developed a gegenbauer reconstruction the partial sums of the fourier or other spectral series are reexpanded as a series of gegenbauer polynomials c n m x recovering spectral accuracy even in the presence of shock waves or other discontinuities to achieve a rate of convergence which is exponential in n however gegenbauer reconstruction requires increasing the order m of the polynomials linearly with the truncation n of the series m bn for some constant b 0 when the order m is fixed it is well known that the gegenbauer series converges as n everywhere on x 1 1 if f x the function being expanded is analytic on the interval but what happens in the diagonal limit in which m n tend to infinity simultaneously we show that singularities of f x off the real axis can destroy convergence of this diagonal approximation process in the sense that the error diverges for subintervals of x 1 1 gegenbauer reconstruction must therefore be constrained to use a sufficiently small ratio of order m to truncation n this off axis singularity constraint is likely to impair the effectiveness of the reconstruction in some applications

the extended finite element method xfem for solidification problems an enriched finite element method for the multi dimensional stefan problems is presented in this method the standard finite element basis is enriched with a discontinuity in the derivative of the temperature normal to the interface the approximation can then represent the phase interface and the associated discontinuity in the temperature gradient within an element the phase interface can be evolved without re meshing or the use of artificial heat capacity techniques the interface is described by a level set function that is updated by a stabilized finite element scheme several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method copyright 2001 john wiley sons ltd

a unified approach to compressible and incompressible flows abstract we present a finite element formulation for solving the compressible navier stokes equations which accommodates the use of any set of variables if primitive variables p u t or entropy variables are used the incompressible limit is well behaved therefore one formulation can be used to solve both compressible and incompressible flows

multiscale stabilization for convection diffusion equations with heterogeneous velocity and diffusion coefficients abstract we present a new stabilization technique for multiscale convection diffusion problems stabilization for these problems has been a challenging task especially for the case with high peclet numbers our method is based on a constraint energy minimization idea and the discontinuous petrov galerkin formulation in particular the test functions are constructed by minimizing an appropriate energy subject to certain orthogonality conditions and are related to the trial space the resulting test functions have a localization property and can therefore be computed locally we will prove the stability and present several numerical results our numerical results confirm that our test space gives a good stability in the sense that the solution error is close to the best approximation error

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

third order upwind finite element computation of the incompressible navier stokes equations part i computation of flow around rectangular cylinders abstract aerodynamic behaviours of two dimensional unsteady flows around rectangular cylinders are numerically investigated by third order upwind finite element computation of the incompressible navier stokes equations a turbulence model such as the two equation model is not incorporated in the computational scheme so that the rectangular cylinders at depth breadth ratios from 0 7 to 4 to be considered are located in a uniform flow it is found that the numerical results of flows around the rectangular cylinders obtained by using the third order upwind finite element scheme are in good agreement with other computational and experimental results

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

optimal gegenbauer quadrature over arbitrary integration nodes this paper treats definite integrations numerically using gegenbauer quadratures the novel numerical scheme introduces the idea of exploiting the strengths of the chebyshev legendre and gegenbauer polynomials through a unified approach and using a unique numerical quadrature in particular the developed numerical scheme employs the gegenbauer polynomials to achieve rapid rates of convergence of the quadrature for the small range of the spectral expansion terms for a large scale number of expansion terms the numerical quadrature has the advantage of converging to the optimal chebyshev and legendre quadratures in the l norm and l 2 norm respectively the key idea is to construct the gegenbauer quadrature through discretizations at some optimal sets of points of the gegenbauer gauss gg type in a certain optimality sense we show that the gegenbauer polynomial expansions can produce higher order approximations to the definite integrals 1 x if x dx of a smooth function f x c 1 1 for the small range by minimizing the quadrature error at each integration point x i through a pointwise approach the developed gegenbauer quadrature can be applied for approximating integrals with any arbitrary sets of integration nodes exact integrations are obtained for polynomials of any arbitrary degree n if the number of columns in the developed gegenbauer integration matrix gim is greater than or equal to n the error formula for the gegenbauer quadrature is derived moreover a study on the error bounds and the convergence rate shows that the optimal gegenbauer quadrature exhibits very rapid convergence rates faster than any finite power of the number of gegenbauer expansion terms two efficient computational algorithms are presented for optimally constructing the gegenbauer quadrature we illustrate the high order approximations of the optimal gegenbauer quadrature through extensive numerical experiments including comparisons with conventional chebyshev legendre and gegenbauer polynomial expansion methods the present method is broadly applicable and represents a strong addition to the arsenal of numerical quadrature methods

supg stabilized finite element resolution of the navier stokes equations applications to water treatment engineering in this paper an analysis of the viscous incompressible flow has been carried out from the very definition of the governing equations up to the resolution of some practical problems passing through the comprehensive study of the stabilized finite element techniques used in their resolution as a consequence of this analysis a code based upon a realistic interpretation of the forces has been written which allows for the modelling of the open channel flow with optimum results in the resolution of some benchmark and real flow problems related with the wastewater industry

short note pade gegenbauer suppression of runge phenomenon in the diagonal limit of gegenbauer approximations boyd shows in 3 that for a function with singularities in the imaginary plane the gegenbauer expansion of the function may have runge type oscillations so large that all hope of convergence for the method is lost we consider the use of pade gegenbauer interpolants to resolve these oscillations we describe a fast interpolation based reconstruction for computing the pade gegenbauer approximants and demonstrate its excellent performance on test examples this method resolves the oscillations and restores accuracy to the gegenbauer approximation of a function with singularities in the imaginary plane without measuring the proximity of these off axis singularities