pseudo time stepping methods for space time discontinuous galerkin discretizations of the compressible navier stokes equations the space time discontinuous galerkin discretization of the compressible navier stokes equations results in a non linear system of algebraic equations which we solve with pseudo time stepping methods we show that explicit runge kutta methods developed for the euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality to evaluate its effectiveness we compare with an implicit explicit runge kutta method which does not suffer from the viscous stability constraint we analyze the stability of the methods and illustrate their performance by computing the flow around a 2d airfoil and a 3d delta wing at low and moderate reynolds numbers

the dimensional reduction modelling approach for 3d beams differential equations and finite element solutions based on hellinger reissner principle abstract this paper illustrates an application of the so called dimensional reduction modelling approach to obtain a mixed 3d linear elastic beam model we start from the 3d linear elastic problem formulated through the hellinger reissner functional then we introduce a cross section piecewise polynomial approximation and finally we integrate within the cross section obtaining a beam model that satisfies the cross section equilibrium and could be applied to inhomogeneous bodies with also a non trivial geometries such as l shape cross section moreover the beam model can predict the local effects of both boundary displacement constraints and non homogeneous or concentrated boundary load distributions usually not accurately captured by most of the popular beam models we modify the beam model formulation in order to satisfy the axial compatibility and without violating equilibrium within the cross section then we introduce axis piecewise polynomial approximation and finally we integrate along the beam axis obtaining a beam finite element also the beam finite elements have the capability to describe local effects of constraints and loads moreover the proposed beam finite element describes the stress distribution inside the cross section with high accuracy in addition to the simplicity of the derivation procedure and the very satisfying numerical performances both the beam model and the beam finite element can be refined arbitrarily allowing to adapt the model accuracy to specific needs of practitioners

on a dimensional reduction method i the optimal selection of basis functions abstract this paper is the first in a series of three which analyze an adaptive approximate approach for solving n 1 dimensional boundary value problems by replacing them with systems of equations in n dimensional space in this approach the unknown functions of n 1 variables are projected onto finite linear combinations of functions of just n variables this paper shows how the coefficients of these linear combinations can be chosen optimally author

relative efficiency of unequal versus equal cluster sizes in cluster randomized and multicentre trials cluster randomized and multicentre trials evaluate the effect of a treatment on persons nested within clusters for instance patients within clinics or pupils within schools optimal sample sizes at the cluster centre and person level have been derived under the restrictive assumption of equal sample sizes per cluster this paper addresses the relative efficiency of unequal versus equal cluster sizes in case of cluster randomization and person randomization within clusters starting from maximum likelihood parameter estimation the relative efficiency is investigated numerically for a range of cluster size distributions an approximate formula is presented for computing the relative efficiency as a function of the mean and variance of cluster size and the intraclass correlation which can be used for adjusting the sample size the accuracy of this formula is checked against the numerical results and found to be quite good it is concluded that the loss of efficiency due to variation of cluster sizes rarely exceeds 10 per cent and can be compensated by sampling 11 per cent more clusters

a globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions we analyze a new galerkin finite element method for numerically solving a linear convection dominated convection diffusion problem in two dimensions the method is shown to be convergent uniformly in the perturbation parameter of order h1 2 in a global energy norm which is stronger than the l2 norm this order is optimal in this norm for our choice of trial functions

global pointwise error estimates for uniformly convergent finite element methods for the elliptic boundary layer problem this paper continues our discussion for the anisotropic model problem e2 2u x2 2 y2 a x y u f x y in 1 there we constructed a bilinear finite element method on a shishkin type mesh the method was shown to be convergent independent of the small parameter in the order of n 2ln2n in the l2 norm where n2 is the total number of mesh points in this paper the method is shown to be convergent independent of in the order of n 2ln3 n in the l norm in the whole computational domain which explains the uniform convergence phenomena we found in the numerical results in 1 another numerical experiment is presented here which confirms our theoretical analysis published by elsevier science ltd

an adaptive multitime multigrid algorithm for time periodic flow simulations the multiscale behaviour and multidisciplinary nature of rotorcraft aerodynamics has delayed the introduction of cfd techniques for rotorcraft aerodynamics the numerical dissipation of standard cfd algorithms may destroy tip vortices before blade vortex interaction takes place more advanced cfd algorithms using high order discretization and or local grid refinement are better suited to tackle the problem these algorithms however generally increase the computational complexity of the simulation and their efficiency should be improved before they can be applied to rotorcraft aerodynamics in this paper a four dimensional solution algorithm will be presented which significantly improves the efficiency by exploiting the periodic nature of rotor flows the efficiency of the algorithm is attained by changing a dynamic problem into a static problem which simplifies the coupling with other models blade dynamics and elastics rotor trim allows local grid refinement in space and time without dynamic load balancing issues and solves a periodic problem by construction a three dimensional multigrid algorithm for dg discretisations on curvilinear structured meshes is extended to four dimensional curvilinear meshes with local grid refinement simulations for an oscillating airfoil in subsonic and transonic conditions confirm the performance of the multigrid algorithm and its insensitiveness to highly irregular grid features the temporal stability restriction of the pseudo time step is removed by treating the diagonal term of the time derivative implicitly

the sdfem for a convection diffusion problem with a boundary layer optimal error analysis and enhancement of accuracy the streamline diffusion finite element method sdfem is applied to a convection diffusion problem posed on the unit square using a shishkin rectangular mesh with piecewise bilinear trial functions the hypotheses of the problem exclude interior layers but allow exponential boundary layers an error bound is proved for u i u n sd where u i is the interpolant of the solution u u n is the sdfem solution and cdot sd is the streamline diffusion norm this bound implies that u u n l 2 is of optimal order thereby settling an open question regarding the l 2 accuracy of the sdfem on rectangular meshes furthermore the bound shows that u n is superclose to u i which allows the construction of a simple postprocessing that yields a more accurate solution enhancement of the rate of convergence by using a discrete streamline diffusion norm is also discussed finally the verification of these rates of convergence by numerical experiments is examined and it is shown that this practice is less reliable than was previously believed

relative efficiencies of two stage sampling schemes for mean estimation in multilevel populations when cluster size is informative in multilevel populations there are two types of population means of an outcome variable ie the average of all individual outcomes ignoring cluster membership and the average of cluster specific means to estimate the first mean individuals can be sampled directly with simple random sampling or with two stage sampling tss that is sampling clusters first and then individuals within the sampled clusters when cluster size varies in the population three tss schemes can be considered ie sampling clusters with probability proportional to cluster size and then sampling the same number of individuals per cluster sampling clusters with equal probability and then sampling the same percentage of individuals per cluster and sampling clusters with equal probability and then sampling the same number of individuals per cluster unbiased estimation of the average of all individual outcomes is discussed under each sampling scheme assuming cluster size to be informative furthermore the three tss schemes are compared in terms of efficiency with each other and with simple random sampling under the constraint of a fixed total sample size the relative efficiency of the sampling schemes is shown to vary across different cluster size distributions however sampling clusters with probability proportional to size is the most efficient tss scheme for many cluster size distributions model based and design based inference are compared and are shown to give similar results the results are applied to the distribution of high school size in italy and the distribution of patient list size for general practices in england

galerkin finite element methods for convection diffusion problems with exponential layers on shishkin triangular meshes and hybrid meshes abstract in this work we provide a convergence analysis for a galerkin finite element method on a shishkin triangular mesh and a hybrid mesh for a singularly perturbed convection diffusion equation the hybrid mesh replaces the triangles of the shishkin mesh by rectangles in the layer regions the supercloseness results are established that the computed solution converges to the interpolant of the true solution with 3 2 order and 2 order up to a logarithmic factor on the two kinds of mesh respectively these convergence rates are uniformly valid with respect to the diffusion parameter and imply that the hybrid mesh is superior to the shishkin triangular mesh numerical experiments illustrate these theoretical results

a note on iterative methods for solving singularly perturbed problems using non monotone methods on shishkin meshes abstract non monotone methods with shishkin meshes are employed in obtaining finite difference schemes for solving a linear two dimensional steady state convection diffusion problem preconditioners are used that significantly reduce the number of iterations of the linear solver computational results for a galerkin method are presented which indicate parameter robust super linear orders of convergence

a fractional step solution method for the unsteady incompressible navier stokes equations in generalized coordinate systems abstract a fractional step method is developed for solving the time dependent three dimensional incompressible navier stokes equations in generalized coordinate systems the primitive variable formulation uses the pressure defined at the center of the computational cell and the volume fluxes across the faces of the cells as the dependent variables instead of the cartesian components of the velocity this choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell the governing equations are discretized by finite volumes using a staggered mesh system the solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a poisson equation this procedure combined with a consistent approximation of the geometric quantities is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain the favorable convergence properties of the poisson solver the momentum equations are solved by an approximate factorization method and a novel zebra scheme with four color ordering is devised for the efficient solution of the poisson equation several two and three dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method good agreement is obtained in all cases

h multigrid for space time discontinuous galerkin discretizations of the compressible navier stokes equations being implicit in time the space time discontinuous galerkin discretization of the compressible navier stokes equations requires the solution of a non linear system of algebraic equations at each time step the overall performance therefore highly depends on the efficiency of the solver in this article we solve the system of algebraic equations with a h multigrid method using explicit runge kutta relaxation two level fourier analysis of this method for the scalar advection diffusion equation shows convergence factors between 0 5 and 0 75 this motivates its application to the 3d compressible navier stokes equations where numerical experiments show that the computational effort is significantly reduced up to a factor 10 w r t single grid iterations

relative efficiency of unequal cluster sizes in stepped wedge and other trial designs under longitudinal or cross sectional sampling background a cluster trial with unequal cluster sizes often has lower precision than one with equal clusters with a corresponding inflation of the design effect for parallel group trials adjustments to the design effect are available under sampling models with a single intracluster correlation design effects for equal clusters under more complex scenarios have appeared recently including stepped wedge trials under cross sectional or longitudinal sampling we investigate the impact of unequal cluster size in these more general settings results assuming a linear mixed model with an exchangeable correlation structure that incorporates cluster and subject autocorrelation we compute the relative efficiency re of a trial with clusters of unequal size under a size stratified randomization scheme as compared to an equal cluster trial with the same total number of observations if there are no within cluster time effects the re exceeds that for a parallel trial in general the re is a weighted average of the re for a parallel trial and the re for a crossover trial in the same clusters existing approximations for parallel designs are extended to the general setting increasing the cluster size by the factor 1 cv2 where cv is the coefficient of variation of cluster size leads to conservative sample sizes as in a popular method for parallel trials conclusion methods to assess experimental precision for single period parallel trials with unequal cluster sizes can be extended to stepped wedge and other complete layouts under longitudinal or cross sectional sampling in practice the loss of precision due to unequal cluster sizes is unlikely to exceed 12

on the relative position of twist and shear centres in the orthotropic and fiberwise homogeneous saint venant beam theory abstract the relationship between twist and shear centres in an orthotropic s aint v enant beam with fiberwise homogeneous elastic moduli and constant poisson ratios is investigated arbitrary cross sections are considered as a new result the relative position of these points is expressed in terms of the scalar potential whose gradient is the rotated field of twist tangential stresses its evaluation requires the solution of n 1 boundary value problems being n 0 the number of holes in the cross section in an isotropic and homogeneous beam the potential is p randtl stress function and known formulae providing the relative position of twist and shear centres are recovered explicit expressions of sliding torsional compliance blocks for t imoshenko beams defined by an energy condition of equivalence with the orthotropic and fiberwise homogeneous s aint v enant theory are provided coincidence of twist centre and t imoshenko shear centre is proven numerical computations on homogeneous and composite orthotropic l sections are performed

on a dimensional reduction method ii some approximation theoretic results abstract this paper is the second in a series of three that analyze a method of dimensional reduction it contains some results for approximation of functions on the interval 1 1 with elements from the nullspace of p to the n power n greater than or equal to 1 where p is a second order ordinary differential operator a special case of this is approximation by polynomials the one dimensional results are used as a tool to prove similar versions in several dimensions these multi dimensional results are directly related to the approximate method of dimensional reduction and they lead to statements about the convergence properties of this approach the third paper which analyzes the adaptive aspects of the method is forthcoming

on asymptotically correct timoshenko like anisotropic beam theory abstract this paper presents a finite element cross sectional beam analysis capable of capturing transverse shear effects the approach uses the variational asymptotic method and can handle beams of general cross sectional shape and arbitrary anisotropic material the work builds on previous works which deal with development of the classical beam theory which includes only extension torsion and bending a timoshenko like formulation is sought to achieve a refined theory with simple boundary conditions apart from some simple special cases it is shown that this problem is overdetermined however it is possible to obtain the best possible solution using the least squares minimization technique the geometrical meaning of the shear variable for this formulation is also derived results are found to be in good agreement with published results for the shear stiffness coefficients for both isotropic and anisotropic beams

necessary convergence conditions for upwind schemes in the two dimensional case this paper considers nine point difference schemes for a two dimensional boundary value singular perturbation problem without turning points and parabolic boundary layers necessary conditions are given for the uniform convergence in the sense of the maximum norm of a scheme using these conditions several widely used schemes are analysed it is shown that some common schemes are not uniformly convergent in and that in some cases we are able to compute uniquely free parameters in the scheme some remarks on the treatment of a problem with a parabolic boundary layer are given

hp multigrid as smoother algorithm for higher order discontinuous galerkin discretizations of advection dominated flows part ii optimization of the runge kutta smoother using a detailed multilevel analysis of the complete hp multigrid as smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator this multilevel analysis is used to optimize the coefficients in the semi implicit runge kutta smoother such that the spectral radius of the multigrid error transformation operator is minimal under properly chosen constraints the runge kutta coefficients for a wide range of cell reynolds numbers and a detailed analysis of the performance of the hp mgs algorithm are presented in addition the computational complexity of the hp mgs algorithm is investigated the hp mgs algorithm is tested on a fourth order accurate space time discontinuous galerkin finite element discretization of the advection diffusion equation for a number of model problems which include thin boundary layers and highly stretched meshes and a non constant advection velocity for all test cases excellent multigrid convergence is obtained

a discontinuous galerkin finite element discretization of the euler equations for compressible and incompressible fluids using the generalized variable formulation of the euler equations of fluid dynamics we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior ideal and real gases can be treated with the same method as an incompressible fluid the well defined incompressible limit relies on using pressure primitive or entropy variables in particular entropy variables can provide numerical methods with attractive properties e g fulfillment of the second law of thermodynamics we show how a discontinuous galerkin finite element discretization previously used for compressible flow with an ideal gas equation of state can be extended for general fluids we also examine which components of the numerical method have to be changed or adapted especially we investigate different possibilities of solving the nonlinear algebraic system with a pseudo time iteration numerical results highlight the applicability of the method for various fluids

a bending gradient model for thick plates part i theory abstract this is the first part of a two part paper dedicated to a new plate theory for out of plane loaded thick plates where the static unknowns are those of the kirchhoff love theory 3 in plane stresses and 3 bending moments to which six components are added representing the gradient of the bending moment the new theory called the bending gradient plate theory is described in the present paper it is an extension to arbitrarily layered plates of the reissner mindlin plate theory which appears as a special case of the bending gradient plate theory when the plate is homogeneous however we demonstrate also that in the general case the bending gradient model cannot be reduced to a reissner mindlin model in part two lebee and sab 2011 the bending gradient theory is applied to multilayered plates and its predictions are compared to those of the reissner mindlin theory and to full 3d pagano s exact solutions the main conclusion of the second part is that the bending gradient gives good predictions of both deflection and shear stress distributions in any material configuration moreover under some symmetry conditions the bending gradient model coincides with the second order approximation of the exact solution as the slenderness ratio l h goes to infinity

convergence in l2 norm of the sdfem on a shishkin triangular mesh for problems with characteristic layers in this paper we analyze a streamline diffusion finite element method sdfem on a shishkin triangular mesh which is applied to a model singularly perturbed convection diffusion problem the main result is to show the sdfem solution on the triangular mesh possesses the optimal convergence order in the l2 norm provided that the diffusion coefficient is sufficiently small compared with the mesh size numerical experiments illustrate the theoretical result

a uniformly convergent galerkin method on a shishkin mesh for a convection diffusion problem abstract a galerkin finite element method that uses piecewise bilinears on a simple piecewise equidistant mesh is applied to a linear convection dominated convection diffusion problem in two dimensions the method is shown to be convergent uniformly in the perturbation parameter of ordern 1 ln nin a global energy norm and of ordern 1 2ln3 2 npointwise near the outflow boundary where the total number of mesh points iso n2

analysis of a beam cross section under coupled actions including transversal shear abstract an efficient finite elements fe based method of cross sectional analysis of a longitudinally homogeneous beam with an arbitrary cross section and material model assumed submitted to tension compression bending torsion and shear is developed a new formulation of this classical problem is done as a special case of the homogenization theory it takes into account 3d strain and stress state fulfilling equilibrium compatibility and constitutive equations at any point stress free conditions on lateral surfaces but preserves control by cross sectional stress resultant forces and corresponding generalized strains a source of problems caused by the presence of a shear force is explained and a way of overcoming it is shown in the paper both variational formulation of the problem and its 2d fe solution are given benchmark cases including shear of a square a composite l section an orthotropic square and an elasto plastic analysis of shearing of a square section show correctness of the method finally two practical cases of application of the method to an analysis of reinforced concrete beam sections are shown

two level fourier analysis of a multigrid approach for discontinuous galerkin discretization in this paper we study a multigrid mg method for the solution of a linear second order elliptic equation discretized by discontinuous galerkin dg methods and we give a detailed analysis of the convergence for different block relaxation strategies we find that pointwise block partitioning gives much better results than the classical cellwise partitioning both for the baumann oden method and for the symmetric dg method with and without interior penalty ip the block relaxation methods jacobi gauss seidel and symmetric gauss seidel give excellent smoothing procedures in a classical mg setting independent of the mesh size simple mg cycles give convergence factors of 0 075 0 4 per iteration sweep for the different discretization methods studied

on timoshenko like modeling of initially curved and twisted composite beams abstract a generalized finite element based cross sectional analysis for nonhomogenous initially curved and twisted anistropic beams is formulated from geometrically nonlinear three dimensional 3 d elasticity the 3 d strain field is formulated based on the concept of decomposition of the rotation tensor and is given in terms of one dimensional 1 d generalized strains and a 3 d warping displacement that is obtained from the formulation not assumed the warping is found in terms of the 1 d strains via the variational asymptotic method vam in this paper a timoshenko like model is presupposed for a beam with cross sectional characteristic length h wavelength of deformation given by l and the magnitude of the radius of initial curvature and or twist is taken to be of the order r first a solution for the asymptotically correct refinement of classical anisotropic beam theory for initially curved and twisted beams through o h2 r2 is obtained next the o h2 l2 correction is computed it is known that timoshenko like theory is not capable of capturing all the o h2 l2 corrections for generally anisotropic beams however if all the o h2 l2 terms are known then the corresponding timoshenko like theory is uniquely defined numerical results are presented to illustrate the trends of the various classical extension twist bending twist and extension bending and nonclassical couplings extension shear bending shear and shear torsion as the initial twist and curvatures are varied

validation of the variational asymptotic beam sectional analysis the computer program vabs variational asymptotic beam section analysis uses the variational asymptotic method to split a three dimensional nonlinear elasticity problem into a twodimensional linear cross sectional analysis and a one dimensional nonlinear beam problem this is accomplished by taking advantage of certain small parameters inherent to beam like structures vabs is able to calculate the one dimensional cross sectional stiffness constants with transverse shear and vlasov refinements for initially twisted and curved beams with arbitrary geometry and material properties several validation cases are presented first an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method and the solution is shown to be identical to that obtained from the theory of elasticity the shear center locations calculated by vabs for various cross sections agree well with those obtained from common engineering analyses comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model for numerical validation values of the one dimensional variables are extracted from an abaqus model and compared with results from a one dimensional beam analysis using cross sectional constants from vabs furthermore point wise three dimensional stress and strain fields are recovered using vabs and the correlation with the three dimensional results from abaqus is excellent finally classical theory is shown to be insufficient for general purpose beam modeling appropriate refined theories are recommended for some classes of problems

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation a new space time discontinuous galerkin finite element method for the solution of the euler equations of gas dynamics in time dependent flow domains is presented the discontinuous galerkin discretization results in an efficient elementwise conservative upwind finite element method which is particularly well suited for local mesh refinement the upwind scheme uses a formulation of the hllc flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated the non linear equations of the space time discretization are solved using a multigrid accelerated pseudo time integration technique with an optimized runge kutta method the linear stability of the pseudo time integration method is investigated for the linear advection equation the numerical scheme is demonstrated with simulations of the flow field in a shock tube a channel with a bump and an oscillating naca 0012 airfoil these simulations show that using the data at the superconvergence points the accuracy of the numerical discretization is o h5 2 in space for smooth subsonic flows both on structured and on locally refined meshes and that the space time adaptation can significantly improve the accuracy and efficiency of the numerical method

shear stresses in prismatic beams with arbitrary cross sections in this paper the approximate computation of shear stresses in prismatic beams due to saint venant torsion and bending using the finite element method is investigated the shape of the considered cross sections may be arbitrary furthermore the basic co ordinate system lies arbitrarily to the centroid and not necessarily in principal directions for numerical reasons dirichlet boundary conditions of the flexure problem are transformed into neumann boundary conditions introducing a conjugate stress function based on the weak formulation of the boundary value problem isoparametric finite elements are formulated the developed procedure yields the relevant warping and torsion constants copyright 1999 john wiley sons ltd

hp multigrid as smoother algorithm for higher order discontinuous galerkin discretizations of advection dominated flows part i multilevel analysis the hp multigrid as smoother algorithm hp mgs for the solution of higher order accurate space time discontinuous galerkin discretizations of advection dominated flows is presented this algorithm combines p multigrid with h multigrid at all p levels where the h multigrid acts as smoother in the p multigrid the performance of the hp mgs algorithm is further improved using semi coarsening in combination with a new semi implicit runge kutta method as smoother a detailed multilevel analysis of the hp mgs algorithm is presented to obtain more insight into the theoretical performance of the algorithm as model problem a fourth order accurate space time discontinuous galerkin discretization of the advection diffusion equation is considered the multilevel analysis shows that the hp mgs algorithm has excellent convergence rates both for steady state and time dependent problems and low and high cell reynolds numbers including highly stretched meshes

a multilevel discontinuous galerkin method a variable v cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented an analysis under a mild regularity assumption shows that the preconditioner is uniform the interior penalty method is then combined with a discontinuous galerkin scheme to arrive at a discretization scheme for an advection diffusion problem for which an error estimate is proved a multigrid algorithm for this method is presented and numerical experiments indicating its robustness with respect to diffusion coefficient are reported

advanced 3d beam element of arbitrary composite cross section including generalized warping effects summary in this paper an advanced 20 20 stiffness matrix and the corresponding nodal load vector of a member of arbitrary composite cross section is developed taking into account shear lag effects due to both flexure and torsion the case of the three dimensional beam element of arbitrary homogeneous cross section is treated as a special one the composite member consists of materials in contact each of which can surround a finite number of inclusions nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions ten boundary value problems with respect to the kinematical components are formulated and solved employing the analog equation method a bem based technique the aforementioned boundary value problems are formulated employing either an improved stress field arising from the correction of shear stress components or the stress field arising directly from displacement considerations the warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure bem approach that is only boundary discretization of the cross section is used numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy the deviations arising from the use of the advanced 20 20 stiffness matrix and the classical 12 12 or 14 14 ones employed in commercial software packages are illustrated through examples of great practical interest moreover the influence of nonuniform warping effects necessitating the use of the aforementioned advanced stiffness matrix is also demonstrated copyright 2015 john wiley sons ltd

an analysis of a conforming exponentially fitted finite element method for a convection diffusion problem in this paper we present a convergence analysis for a conforming exponentially fitted galerkin finite element method with triangular elements for a linear singularly perturbed convection diffusion problem with a singular perturbation parameter e it is shown that the error for the finite element solution in the energy norm is bounded by o h e1 2 u 2 e 1 2 u 1 if a regular family of triangular meshes is used in the case that a problem contains only exponential boundary layers the method is shown to be convergent at a rate of h1 2 h ln e on anisotropic layer fitted meshes

higher order piezoelectric plate theory derived from a three dimensional variational principle a three dimensional mixed variational principle is used toderive a kth order two dimensional lineartheory for an anisotropichomogeneouspiezoelectric pzt plate themechanicaldisplacements theelectricpotential theinplane components of the stress tensor and the in plane components of the electric displacement are expressed as a e niteseries of orderk inthethickness coordinate bytakinglegendrepolynomialsas thebasisfunctions however the transverse shear stress the transverse normal stress and the transverse electric displacement are expressed as a e nite series of order k 2 in the thickness coordinate the formulation accounts for the double forces without moments that may change the thickness of the plate results obtained by using the plate theory are given for the bending of a cantilever thick plate loaded on the top and the bottom surfaces by uniformly distributed 1 normal tractions and 2 tangential tractions results are also computed for the bending of a cantilever thick pzt beam loaded by 1 a uniformly distributed charge density on the top and the bottom surfaces and 2 equal and opposite normal tractions distributed uniformly only on a part of the beam the seventh order plate theory captures well the boundary layer effects near the clamped and the free edges and adjacent to the top and the bottom surfaces of a thick orthotropic cantilever beam with the span to the thickness ratio of two also through the thickness variation of the transverse shear and the transverse normal stresses agree well with those computed from the analytical solution of the three dimensional elasticity equations the governing partial differential equations are second order so that lagrange basis functions can be used to solve the problem by the e nite element method

a parameter robust numerical method for a two dimensional reaction diffusion problem in this paper a singularly perturbed reaction diffusion partial differential equation in two space dimensions is examined by means of an appropriate decomposition we describe the asymptotic behaviour of the solution of problems of this kind a central finite difference scheme is constructed for this problem which involves an appropriate shishkin mesh we prove that the numerical approximations are almost second order uniformly convergent in the maximum norm with respect to the singular perturbation parameter some numerical experiments are given that illustrate in practice the theoretical order of convergence established for the numerical method

sample size calculations for clustered binary data in this paper we propose a sample size calculation method for testing on a binomial proportion when binary observations are dependent within clusters in estimating the binomial proportion in clustered binary data two weighting systems have been popular equal weights to clusters and equal weights to units within clusters when the number of units varies cluster by cluster performance of these two weighting systems depends on the extent of correlation among units within each cluster in addition to them we will also use an optimal weighting method that minimizes the variance of the estimator a sample size formula is derived for each of the estimators with different weighting schemes we apply these methods to the sample size calculation for the sensitivity of a periodontal diagnostic test simulation studies are conducted to evaluate a finite sample performance of the three estimators we also assess the influence of misspecified input parameter values on the calculated sample size the optimal estimator requires equal or smaller sample sizes and is more robust to the misspecification of an input parameter than those assigning equal weights to units or clusters

on the choice of the reference frame for beam section stiffness properties abstract this work discusses the choice of a reference frame for beam section stiffness properties established concepts as the center of elasticity the center of stiffness and the center of compliance are discussed and contextualized an interpretation of univocally defined generalized strain transformations is given in terms of minimization of appropriate norms of the stiffness and compliance matrices of the beam section that univocally define special reference points transformations of generalized strain perturbations that preserve the angular strain are sought they are subsequently constrained to represent a change of reference point and further restricted to lie in the plane of the section each transformation is univocally defined and given a clear mathematical and geometrical interpretation it is recognized that transformations that decouple forces and linear strains from moments and angular strains cannot be described as a mere change of reference point

a global uniformly convergent finite element method for a quasi linear singularly perturbed elliptic problem abstract in this paper we construct a bilinear finite element method based on a special piecewise uniform mesh for solving a quasi linear singularly perturbed elliptic problem in two space dimensions a quasi optimal global uniform convergence rate o n 2x ln2 nx n 2y ln2 ny was obtained which is independent of the perturbation parameter here nx and ny are the number of elements in the x and y directions respectively

a space time hybridizable discontinuous galerkin method for incompressible flows on deforming domains we present the first space time hybridizable discontinuous galerkin hdg finite element method for the incompressible navier stokes and oseen equations major advantages of a space time formulation are its excellent capabilities of dealing with moving and deforming domains and grids and its ability to achieve higher order accurate approximations in both time and space by simply increasing the order of polynomial approximation in the space time elements our formulation is related to the hdg formulation for incompressible flows introduced recently in e g n c nguyen j peraire b cockburn a hybridizable discontinuous galerkin method for stokes flow comput methods appl mech eng 199 2010 582 597 however ours is inspired in typical dg formulations for compressible flows which allow for a more straightforward implementation another difference is the use of polynomials of fixed total degree with space time hexahedral and quadrilateral elements instead of simplicial elements we present numerical experiments in order to assess the quality of the performance of the methods on deforming domains and to experimentally investigate the behavior of the convergence rates of each component of the solution with respect to the polynomial degree of the approximations in both space and time

optimal runge kutta smoothers for the p multigrid discontinuous galerkin solution of the 1d euler equations this work presents a family of original runge kutta methods specifically designed to be effective relaxation schemes in the numerical solution of the steady state solution of purely advective problems with a high order accurate discontinuous galerkin space discretization and a p multigrid solution algorithm the design criterion for the construction of the runge kutta methods here developed is different form the one traditionally used to derive optimal runge kutta smoothers for the h multigrid algorithm which are designed in order to provide a uniform damping of the error modes in the high frequency range only the method here proposed is instead designed in order to provide a variable amount of damping of the error modes over the entire frequency spectrum the performance of the proposed schemes is assessed in the solution of the steady state quasi one dimensional euler equations for two test cases of increasing difficulty some preliminary results showing the performance for multidimensional applications are also presented

finite element superconvergence on shishkin mesh for 2 d convection diffusion problems in this work the bilinear finite element method on a shishkin mesh for convection diffusion problems is analyzed in the two dimensional setting a superconvergence rate o n 2 ln2 n en 1 5lnn in a discrete e weighted energy norm is established under certain regularity assumptions this convergence rate is uniformly valid with respect to the singular perturbation parameter e numerical tests indicate that the rate o n 2ln2 n is sharp for the boundary layer terms as a by product an e uniform convergence of the same order is obtained for the l2 norm furthermore under the same regularity assumption an e uniform convergence of order n 3 2ln5 2n en 1ln1 2n in the l norm is proved for some mesh points in the boundary layer region

accounting for expected attrition in the planning of community intervention trials trials in which intact communities are the units of randomization are increasingly being used to evaluate interventions which are more naturally administered at the community level or when there is a substantial risk of treatment contamination in this article we focus on the planning of community intervention trials in which k communities for example medical practices worksites or villages are to be randomly allocated to each of an intervention and a control group and fixed cohorts of m individuals enrolled in each community prior to randomization formulas to determine k or m may be obtained by adjusting standard sample size formulas to account for the intracluster correlation coefficient rho in the presence of individual level attrition however observed cohort sizes are likely to vary we show that conventional approaches of accounting for potential attrition such as dividing standard sample size formulas by the anticipated follow up rate pi or using the average anticipated cohort size m pi may respectively overestimate or underestimate the required sample size when cluster follow up rates are highly variable and m or rho are large we present new sample size estimation formulas for the comparison of two means or two proportions which appropriately account for variation among cluster follow up rates these formulas are derived by specifying a model for the binary missingness indicators under the population averaged approach assuming an exchangeable intracluster correlation coefficient denoted by tau to aid in the planning of future trials we recommend that estimates for tau be reported in published community intervention trials

shishkin mesh simulation a new stabilization technique for convection diffusion problems abstract a new stabilization procedure is presented it is based on a simulation of the interaction between the coarse and fine parts of a shishkin mesh but can be applied on coarse and irregular meshes and on domains with nontrivial geometries the technique which does not require adjusting any parameter can be applied to different stabilized and non stabilized methods numerical experiments show it to obtain oscillation free approximations on problems with boundary and internal layers on uniform and nonuniform meshes and on domains with curved boundaries

finite element approximation of convection diffusion problems using an exponentially graded mesh we present the analysis of an h version finite element method for the approximation of the solution to convection diffusion problems the method uses piece wise polynomials of degree p 1 defined on an exponentially graded mesh optimally constructed for the approximation of exponential layers we consider a model convection diffusion problem posed on the unit square and establish robust optimal convergence rates in the energy and in the maximum norm we also present the results of some numerical computations that illustrate our theoretical findings and compare the proposed method with others found in the literature

space time discontinuous galerkin method for the compressible navier stokes equations a space time discontinuous galerkin finite element method for the compressible navier stokes equations is presented we explain the space time setting derive the weak formulation and discuss our choices for the numerical fluxes the resulting numerical method allows local grid adaptation as well as moving and deforming boundaries which we illustrate by computing the flow around a 3d delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2d airfoil in rapid pitch up maneuver

sample size in cluster randomized trials with time to event as the primary endpoint in cluster randomized trials groups of individuals clusters are randomized to the treatments or interventions to be compared in many of those trials the primary objective is to compare the time for an event to occur between randomized groups and the shared frailty model well fits clustered time to event data members of the same cluster tend to be more similar than members of different clusters causing correlations as correlations affect the power of a trial to detect intervention effects the clustered design has to be considered in planning the sample size in this publication we derive a sample size formula for clustered time to event data with constant marginal baseline hazards and correlation within clusters induced by a shared frailty term the sample size formula is easy to apply and can be interpreted as an extension of the widely used schoenfeld s formula accounting for the clustered design of the trial simulations confirm the validity of the formula and its use also for non constant marginal baseline hazards findings are illustrated on a cluster randomized trial investigating methods of disseminating quality improvement to addiction treatment centers in the usa copyright 2012 john wiley sons ltd

on solution strategies to saint venant problem different solution strategies to the relaxed saint venant problem are presented and comparatively discussed from a mechanical and computational point of view three approaches are considered namely the displacement approach the mixed approach and the modified potential stress approach the different solution strategies lead to the formulation of two dimensional neumann and dirichlet boundary value problems several solution strategies are discussed in general namely the series approach the reformulation of the boundary value problems for the laplace s equations as integral boundary equations and the finite element approach in particular the signatures of the finite element weak solutions the computational costs the convergence the accuracy are discussed considering elastic cylinders whose cross sections are represented by piece wise smooth domains

sample size adjustments for varying cluster sizes in cluster randomized trials with binary outcomes analyzed with second order pql mixed logistic regression adjustments of sample size formulas are given for varying cluster sizes in cluster randomized trials with a binary outcome when testing the treatment effect with mixed effects logistic regression using second order penalized quasi likelihood estimation pql starting from first order marginal quasi likelihood mql estimation of the treatment effect the asymptotic relative efficiency of unequal versus equal cluster sizes is derived a monte carlo simulation study shows this asymptotic relative efficiency to be rather accurate for realistic sample sizes when employing second order pql an approximate simpler formula is presented to estimate the efficiency loss due to varying cluster sizes when planning a trial in many cases sampling 14 per cent more clusters is sufficient to repair the efficiency loss due to varying cluster sizes since current closed form formulas for sample size calculation are based on first order mql planning a trial also requires a conversion factor to obtain the variance of the second order pql estimator in a second monte carlo study this conversion factor turned out to be 1 25 at most

a uniformly convergent continuous discontinuous galerkin method for singularly perturbed problems of convection diffusion type abstract in this paper we introduce a coupled approach of local discontinuous galerkin and standard finite element method for solving singularly perturbed convection diffusion problems on shishkin mesh with linear elements a rate o n 1 ln n in an associated norm is established where n is the number of elements numerical experiments complement the theoretical results moreover a rate o n 2 ln 2 n in a discrete l norm and o n 2 in l2 norm are observed numerically on the shishkin mesh

optimal convergence of basic schemes for elliptic boundary value problems with strong parabolic layers we consider a convection diffusion problem with strong parabolic boundary layers and its discretization using upwind finite differences or bilinear finite elements on a layer adapted mesh based on a new decomposition of the solution we are able to prove optimal uniform convergence results

plane wave solutions and modal analysis in higher order shear and normal deformable plate theories abstract we use the three dimensional hellinger reissner mixed variational principle to derive a k th order k 0 1 2 shear and normal deformable plate theory the balance laws the constitutive relations and the boundary conditions for the plate theory are deduced the constitutive relations incorporate the shear and the normal tractions applied on the top and the bottom surfaces of the plate for a k th order plate theory with displacements expressed as a power series in the thickness co ordinate z with terms up to z k the transverse shear and the transverse normal stresses involve terms upto z k 2 while in plane stress components have terms up to z k the equations for the plate theory are expressed in a compact form by taking legendre polynomials as the basis functions the plate theory is used to study plane travelling waves and in particular the lengths of decay of the displacement components this allows for a rigorous ordering of the importance of the displacement descriptors in terms of decaying properties finally we study the free vibrations of a simply supported rectangular orthotropic thick plate results from the present theory are compared with an exact three dimensional solution and with other plate theories to this end a k th order compatible plate theory is also deduced the term compatible alludes to the fact that the reduction map for the stress fields is induced by the kinematical reduction map whilst in the mixed models it is postulated independently it is found that the frequencies up to the fifth mode of vibration computed with the fifth order theory and without introducing any shear correction factors match very well with the corresponding analytical solution also through the thickness distribution of all of the stress components is found to agree well with the three dimensional elasticitysolution while the stress distribution obtained from the compatible plate theories deviatesconsiderably especially for the higher modes

a novel nonconforming uniformly convergent finite element method in two dimensions we give an new analysis of a nonconforming galerkin finite element method for solving linear singularly perturbed two dimensional boundary value problems without turning points the method is shown to be convergent uniformly in the perturbation parameter of order h 1 2 in an energy norm the trial functions used are exponentials adapted to the differential operator