finite element solution of compressible viscous flows using conservative variables abstract a finite element method for solving the compressible navier stokes equations is presented these equations are solved in conservation form and using conservative variables appropriate finite element approximations are discussed when a galerkin variational formulation is used for high speed flows the formulation is stabilized using the stream line upwind petrov galerkin method for which we propose an analytical expression for the matrix a new discontinuity capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients the non linear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual gmres algorithm numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed finite element method

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

theories of causal ordering abstract this paper is a response to iwasaki and simon 14 which criticizes de kleer and brown 8 we argue that many of their criticisms particularly concerning causality modeling and stability originate from the difference of concerns between engineering and economics our notion of causality arises from considering the interconnections of components not equations when no feedback is present the ordering produced by our qualitative physics is similar to theirs however when feedback is present our qualitative physics determines a causal ordering around feedback loops as well causal ordering is a general technique not only applicable to qualitative reasoning therefore we also explore the relationship between causal ordering and propagation of constraints upon which the methods of qualitative physics are based

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

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

an unstructured finite elements method for solving the compressible rans equations and the spalart allmaras turbulence model this paper deals with a stabilized finite element method for solving the compressible navier stokes equations combined with the spalart allmaras turbulence model the aim is to assess the ability of this formulation to solve high reynolds number turbulent flows over anisotropic meshes this formulation lies in the framework of the stream line upwind petrove galerkin method we propose a simple and efficient formulation for the stabilization matrix and develop a shock capturing operator numerical tests on the 3d boundary layer over a flat plate and on the onera m6 wing show the stability and robustness of the proposed method

time discontinuous stabilized space time finite elements for timoshenko beams stabilized space time e nite element methods for the transient computational analysis of the elastodynamics of timoshenko beams have been developed the underlying time discontinuous galerkin formulation is implicit unconditionally stable higher order accurate and robust the employed interpolations are continuous in space and time inside time slabs but discontinuous in time between adjacent time slabs to suppress spurious numerical oscillations near discontinuities or high gradients galerkin least squares stabilization has been applied further improvement of the numerical representation of the transient elastic wave propagation phenomena has been achieved by specially designed galerkin gradient least squares operators because of the reduced phase and amplitude errors of these e nite elements much coarser spatial meshes may be used without loss of accuracy the resulting reduction of the number of unknowns leads to a signie cant decrease of computer time furthermore a globaladaptivetime stepping strategy has beenemployed basedon thetemporal jump residual of thetimee niteelement method as error estimator numerical examples of transientelastic wave propagation in timoshenko beams involving a wide spectrum of wave numbers and frequencies demonstrate the good performance of the developed methods

physics based gmres preconditioner for compressible and incompressible navier stokes equations abstract this paper presents the implementation of a local physics preconditioning mass matrix 8 for an unified approach of 3d compressible and incompressible navier stokes equations using an supg finite element formulation and gmres implicit solver during the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of mach and reynolds numbers 10 26 37 on the other hand supg finite element formulation and gmres implicit solver is one of the most robust combinations to solve state of the art cfd problems 1 6 9 22 29 30 31 the selection of a good preconditioner and its performance on parallel architecture is another open problem in cfd community the local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of mach and reynolds numbers being very suitable for massively parallel computations finally it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning

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

causality analysis of neural connectivity critical examination of existing methods and advances of new methods granger causality gc is one of the most popular measures to reveal causality influence of time series and has been widely applied in economics and neuroscience especially its counterpart in frequency domain spectral gc as well as other granger like causality measures have recently been applied to study causal interactions between brain areas in different frequency ranges during cognitive and perceptual tasks in this paper we show that 1 gc in time domain cannot correctly determine how strongly one time series influences the other when there is directional causality between two time series and 2 spectral gc and other granger like causality measures have inherent shortcomings and or limitations because of the use of the transfer function or its inverse matrix and partial information of the linear regression model on the other hand we propose two novel causality measures in time and frequency domains for the linear regression model called new causality and new spectral causality respectively which are more reasonable and understandable than gc or granger like measures especially from one simple example we point out that in time domain both new causality and gc adopt the concept of proportion but they are defined on two different equations where one equation for gc is only part of the other for new causality thus the new causality is a natural extension of gc and has a sound conceptual theoretical basis and gc is not the desired causal influence at all by several examples we confirm that new causality measures have distinct advantages over gc or granger like measures finally we conduct event related potential causality analysis for a subject with intracranial depth electrodes undergoing evaluation for epilepsy surgery and show that in the frequency domain all measures reveal significant directional event related causality but the result from new spectral causality is consistent with event related time frequency power spectrum activity the spectral gc as well as other granger like measures are shown to generate misleading results the proposed new causality measures may have wide potential applications in economics and neuroscience

simple stabilizing matrices for the computation of compressible flows in primitive variables the key ingredient that balances stability and accuracy in stabilized formulations is the parameter of intrinsic time scales for multi dimensional hyperbolic systems of equations this parameter is a matrix and the available expressions for its computation involve the solution of an eigenvalue problem which can be tedious or cpu time consuming thus for formulations based on primitive variables including pressure a couple of simple stabilizing matrices are presented which are easy to implement and cpu economic numerical evaluations show the performance of the various choices

the determination of the leading coefficient in the monotone potential sturm liouville operator from boundary measurements this paper deals with the problem of determining the leading coefficient k k u 2 of the nonlinear monotone potential sturm liouville operator au k u 2 u x q x u x x a b as an additional condition only two measured data at the boundary x a x b are used solvability and linearization of the corresponding nonlinear direct problem are given an existence of a quasi solution of the inverse problem is obtained in a suitable compact class of admissible coefficients in the second part of the paper an approximate analytical solution for the inverse problem is derived the approach presented permits to analyze well posed as well as all ill posed situations for the inverse coefficient problem numerical examples corresponding to the all considered situations are presented

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

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 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

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

determination of leading coefficients in sturm liouville operator from boundary measurements ii unicity and an engineering approach we study the problem of determining the leading coefficient k k x of the sturm liouville operator au k x u x q x u x x a b from a measured data given in the form of dirichlet or and neumann type additional boundary conditions the contribution of the each measured data to the unicity of the inverse problem solution is analysed based on the analysis the problem is treated as a cauchy problem for the first order ordinary differential equation with respect to k x for the case when the direct problem solution u u x belongs to the class of the second order polynomials and u x 0 we present an analytical formula for an approximate solution of the inverse problem numerical examples related to accuracy of the solution and to essential features of the inverse problem are demonstrated

convexity argument for monotone potential operators and its application modelling of many applied problems leads to the nonlinear equations elliptic type with monotone potential operators 6 11 some methods have been developed for di erent classes of nonlinear operators to study such qualitative questions as existence uniqueness linearization of the nonlinear operator and convergence of an approximate solution 2 7 11 in some cases it is possible to construct an abstract iteration technique for linearization of the nonlinear operator and to prove the convergence of an approximate solution in this paper we prove an abstract iterative scheme for monotone potential operators by using the convexity argument note that in the literature di erent convexity arguments or inequalities have been applied to problems of mathematical physics 14 in particular in 9 10 the logarithmic convexity argument was used to establish continuous dependence on the initial data for the cauchy problem the convexity argument introduced here is used as a su cient condition for the convergence of the abstract iteration scheme for monotone potential operators then using the result the convergence of the iteration scheme is proved for concrete nonlinear problems the paper is organized as follows in section 2 we introduce the functional inequality which is called the convexity argument then we consider an abstract operator equation and by using the argument we prove the strong convergence of the iteration

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

an inverse eigenvalue problem for a vibrating string with two dirichlet spectra a classical inverse problem is can you hear the density of a string clamped at both ends the mathematical model gives rise to an inverse sturm liouville problem for the unknown density rho and it is well known that the answer is negative the dirichlet spectrum from the clamped end point conditions is insufficient there are many known ways to add additional information to gain a positive answer and these include changing one of the boundary conditions and recomputing the spectrum or giving the energy in each eigenmode the so called norming constants we make the assumption that neither of these changes are possible instead we will add known mass densities to the string in a way we can prescribe and remeasure the dirichlet spectrum we will not be able to answer the uniqueness question in its most general form but will give some insight to what added masses should be chosen and how this can lead to a reconstruction of the original string density

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

recovering the density of a string from only lowest frequency data a classical inverse problem is can you hear the density of a string clamped at both ends the answer as narrowly stated is negative one has to give an additional data sequence such as the energy in each mode norming constants or information on the string slope at the endpoints or alternatively change the boundary conditions and obtain the new frequencies what if neither of these options is possible one solution recently proposed was to add a known mass density and remeasure the dirichlet spectrum w rundell and p e sacks siam j appl math 73 2013 pp 1020 1037 in this work we take a related approach we are able to add any number of known mass densities but we can only measure the fundamental frequency that is the lowest eigenvalue in each case we will show that our problem can be closely approximated by a related problem for which there is uniqueness and we discuss a suite of reconstruction methods

causality in device behavior abstract this paper shows how formal characterizations of causality and of the method of comparative statics long used in econometrics thermodynamics and other domains can be applied to clarify and make rigorous the qualitative causal calculus recently proposed by de kleer and brown 2 the formalization shows exactly what assumptions are required to carry out causal analysis of a system of interdependent variables in equilibrium and to propagate disturbances through such a system the intuitive concepts of causality captured by de kleer and brown provide a rough approximation to the standard analytic techniques that are used in the treatment of simultaneous algebraic and differential equations

an inverse problem for a sturm liouville operator if 0 is not a dirichlet eigenvalue of the sturm liouville operator d2 dx2 q x on 0 1 then q x l2 0 1 is uniquely determined by the data u j 0 j 1 where uj x solves u j x q x uj x j x 0 x 1uj 0 0uj 1 0 and j x j 1 is a basis of l2 0 1 numerical approximations of q x using finite data are constructed

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

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 neural network model of causality this paper proposes a model for commonsense causal reasoning based on the basic idea of neural networks after an analysis of the advantages and limitations of existing accounts of causality a fuzzy logic based formalism fel is proposed that takes into account the inexactness and the cumulative evidentiality of commonsense causal reasoning overcoming the limitations of existing accounts analyses concerning how fel handles various aspects of commonsense causal reasoning are performed in an abstract way fel can be implemented naturally in a neural connectionist network this work also serves to link rule based reasoning with neural network models in that a rule encoding scheme fel is equated directly to a neural network model

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

mass corrections for the conservative coupling of flow and transport on collocated meshes buoyancy driven flow models demand a careful treatment of the mass balance equation to avoid spurious source and sink terms in the non linear coupling between flow and transport in the context of finite elements it is therefore commonly proposed to employ sufficiently rich pressure spaces containing piecewise constant shape functions to obtain local or even strong mass conservation in three dimensional computations this usually requires nonconforming approaches special meshes or higher order velocities which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code in this paper we therefore propose a lean and conservatively coupled scheme based on standard stabilized linear equal order finite elements for the stokes part and vertex centered finite volumes for the energy equation we show that in a weak mass balance it is possible to recover exact conservation properties by a local flux correction which can be computed efficiently on the control volume boundaries of the transport mesh we discuss implementation aspects and demonstrate the effectiveness of the flux correction by different two and three dimensional examples which are motivated by geophysical applications

solution techniques for multi physics problems with application to computational nonlinear aeroelasticity this paper presents an efficient parallel distributed methodology for solving multi physic problems this methodology is based on functional and geometric decompositions solution algorithms for coupled problems are discussed all these techniques are illustrated for the case of cfd based aeroelasticity a numerical study is performed for the agrad 445 6 aeroelastic test case 2005 elsevier ltd all rights reserved

a fully coupled rans spalart allmaras supg formulation for turbulent compressible flows on stretched unstructured grids abstract when high reynolds turbulent flows are combined with complex and large size geometries computers are no longer enough powerful to deal with direct numerical simulation dns and with the resolution of all the scales of turbulence motion therefore the rans approaches solve averaged equations and use a model to simulate these scales this model contains dissipation processes that should not be polluted by the numerical diffusion needed to stabilized approximations for convection dominated flows in this paper we proposed a strongly coupled numerical formulation for the spalart allmaras model in the framework of stabilized finite element methods computations are performed for compressible newtonian fluids 2d and 3d on unstructured grids of high aspect ratio results are compared with experimental data and also with solutions obtained by different numerical strategies

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 first order hyperbolic framework for large strain computational solid dynamics part i total lagrangian isothermal elasticity abstract this paper introduces a new computational framework for the analysis of large strain fast solid dynamics the paper builds upon previous work published by the authors gil et al 2014 48 where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic materials in terms of the linear momentum the deformation gradient and its jacobian as unknown variables in this work the formulation is further enhanced with four key novelties first the use of a new geometric conservation law for the co factor of the deformation leads to an enhanced mixed formulation advantageous in those scenarios where the co factor plays a dominant role second the use of polyconvex strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes for solid dynamics problems moreover the introduction of suitable conjugate entropy variables enables the derivation of a symmetric system of hyperbolic equations dual of that expressed in terms of conservation variables third the new use of a tensor cross product 61 greatly facilitates the algebraic manipulations of expressions involving the co factor of the deformation fourth the development of a stabilised petrov galerkin framework is presented for both systems of hyperbolic equations that is when expressed in terms of either conservation or entropy variables as an example a polyconvex mooney rivlin material is used and for completeness the eigen structure of the resulting system of equations is studied to guarantee the existence of real wave speeds finally a series of numerical examples is presented in order to assess the robustness and accuracy of the new mixed methodology benchmarking it against an ample spectrum of alternative numerical strategies including implicit multi field fraeijs de veubeke hu washizu variational type approaches and explicit cell and vertex centred finite volume schemes

the determination of a coefficient in an elliptic equation from average flux data abstract we consider the question of recovering the coefficient q from the equation u j q x u j j x subject to homogeneous dirichlet boundary conditions in a bounded domain r 2 the nonhomogeneous source terms j x j 1 form a basis for l 2 it will be proven that a unique determination is possible from data measurements consisting of measurements of the net flux r uj vds 1 leaving a subset of the boundary for each input source j a continuous dependence result and an algorithm that allows efficient numerical reconstruction of q x from finite data is presented

a globally convergent matrix free algorithm for implicit time marching schemes arising in finite element analysis in fluids a solution procedure for solving nonlinear time marching problems is presented the nonsymmetric systems of equations arising from a newton type linearization of these time marching problems are solved using an iterative strategy based on the generalized minimal residual gmres algorithm matrix free techniques leading to reduction in storage are presented incorporation of a linesearch algorithm in the newton gmres scheme is discussed an automatic time increment control strategy is developed to increase the stability of the time marching process high speed flow computations demonstrate the effectiveness of these algorithms

on a parabolic quadrilateral finite element for compressible flows abstract we present a 9 node finite element for compressible flow solutions a high order derivative upwind term and a shock capturing term are employed for stability and accuracy of the formulation we give the solutions of various example problems to illustrate our experiences with the element

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

determination of leading coefficients in sturm liouville operator from boundary measurements i a stripping algorithm we present a stripping algorithm for determination of the unknown coefficient k k x in the sturm liouville operator au k x u x q x u x email protected a b form boundary measurements due to the only two physically possible measured data at the boundary the problem is of strong unstable the formulation of the problem based on the tikhonov s quasisolution approach the coefficient k x l 2 a b is assumed to be a monotone and uniform bounded function this class of functions k c is compact in l 2 a b and hence the inverse problem has at least one quasisolution in k c the stripping algorithm is implemented for the cases when the unknown function k x is interpolated by the first and second order polynomials effectiveness of the method is demonstrated on concrete numerical examples with exact and noisy data

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