adaptive remeshing and h p domain decomposition abstract the h p version of the finite element method combines local mesh refinement with an increase of the shape functions polynomial degree this paper presents a method which uses an h p approximation for a domain decomposition with fully overlapping domains allowing c 0 continuous approximation for geometrically incompatible mesh refinement to be obtained the method is applied to a reaction diffusion problem resulting from semiconductor process simulation in numerical examples it is demonstrated that this approach is well suited for problems with sharp interior layers or shock like behaviour

p version plate and curved shell element for geometrically non linear analysis this paper presents a p version geometrically non linear formulation based on the total lagrangian approach for a nine node three dimensional curved shell element the element geometry is defined by the coordinates of the nodes located on its middle surface and nodal vectors describing the bottom and top surfaces of the element the element displacement approximation can be of arbitrary and different polynomial orders in the plane of the element and in the transverse direction the element approximation functions and the corresponding nodal variables are derived from the lagrange family of interpolation functions the resulting approximation functions and the nodal variables are hierarchical and the element displacement approximation ensures c continuity the element properties are established using the principle of virtual work and the hierarchical element approximation in formulating the properties of the element complete three dimensional stresses and strains are considered hence the element is equally effective for very thin as well as extremely thick shells and plates incremental equations of equilibrium are derived and solved using the standard newton raphson method the total load is divided into increments and for each increment of load equilibrium iterations are performed until each component of the residuals is within a preset tolerance numerical examples are presented to show the accuracy efficiency and advantages of the present formulation the results obtained from the present formulation are compared with those available in the literature

definition of a p interpolating space of hierarchical bases of finite elements on the pyramid abstract this article shows in detail how to construct in a simple and ordered way a set of rational functions defined on the pyramid topology the set of functions is parameterized by an integer p it is shown that these functions defined in a hierarchical way constitute a basis for a complete polynomial interpolation space of degree p on the pyramid domain in order to help this definition we use a denumerable sequence of orthogonal polynomials defined on an interval of the real line a priori any increasing sequence of polynomials in one variable can be used the bases are constructed to be used in the class c 0 method of finite elements the rational functions thus defined can be combined to represent any polynomial of degree p thus given an arbitrary number p one defines a finite element whose geometry is a pyramid that has associated a complete interpolation space of degree p moreover this element is adequate to be used with the p adaptive technique on heterogeneous meshes of finite elements hierarchical

theh p version of the finite element method for elliptic equations of order2m the problems of elliptic partial differential equations stemming from engineering problems are usually characterized by piecewise analytic data it has been shown in 3 4 5 that the solutions of the second order and fourth order equations belong to the spacesb 1 where the weighted sobolev norms of thek th derivatives are bounded bycd k l k l k l l 2 wherec andd are constants independent ofk in this case theh p version of the finite element method leads to an exponential rate of convergence measured in the energy norm 6 12 13 theh p version was implemented in the code probe1 18 and has been very successfully used in the industry we will discuss in this paper the generalization of these results for problems of order2m we will show also that the exponential rate can be achieved if the exact solution belongs to the spacesb 1 where the weighted sobolev norm of thek th derivatives is bounded bycd k l k l k l m 1 c andd are independent ofk in addition if the data is piecewise analytic then in fact the exact solution belongs to the spacesb m 1 problems of this type are related obviously to many engineering problems such as problems of plates and shells and are also important in connection with well known locking problems

two bracketing theorems characterizing the eigensolution for theh version of the finite element method this paper demonstrates that the classical inclusion principle is in general not valid for the h version of the finite element method whereas the inclusion principle is valid for second order systems discretized by the h version of the finite element method provided linear interpolation functions are used as admissible functions the principle is not valid for fourth order systems to characterize the computed eigenvalues for fourth order systems discretized by the h version of the finite element method this paper formulates two bracketing theorems

lp estimates on functions of the laplace operator on etudie la continuite l p de certaines fonctions du laplacien sur une variete de riemann complete a geometrie bornee

new basis functions and computational procedures for p version finite element analysis new basis functions and solution procedures for p version finite element analysis are described they are used in a highly efficient p version finite element solver for linear elastostatics and dynamics which has been used in an industrial environment for over two years using two sample applications it is shown that using the techniques proposed here p version finite element analysis can have a substantially lower computational cost for given accuracy than standard finite element methods this makes the industrial applicability of p version finite element analysis much wider than is commonly believed

a comment on the effectiveness of uniform finite element refinements on presente des resultats numeriques sur l utilisation d approches de raffinement h pour la resolution de problemes d elasticite avec singularites et on les compare avec des resultats recents bases sur l approche de raffinement p

using a mixed integer quadratic programming solver for the unconstrained quadratic 0 1 problem in this paper we consider problem p of minimizing a quadratic function q x x tqx ctx of binary variables our main idea is to use the recent mixed integer quadratic programming miqp solvers but for this we have to first convexify the objective function q x a classical trick is to raise up the diagonal entries of q by a vector u until q diag u is positive semidefinite then using the fact that xi2 xi we can obtain an equivalent convex objective function which can then be handled by an miqp solver hence computing a suitable vector u constitutes a preprocessing phase in this exact solution method we devise two different preprocessing methods the first one is straightforward and consists in computing the smallest eigenvalue of q in the second method vector u is obtained once a classical sdp relaxation of p is solved we carry out computational tests using the generator of pardalos and rodgers 1990 and we compare our two solution methods to several other exact solution methods furthermore we report computational results for the max cut problem

higher order multi resolution topology optimization using the finite cell method this article presents a detailed study on the potential and limitations of performing higher order multi resolution topology optimization with the finite cell method to circumvent stiffness overestimation in high contrast topologies a length scale is applied on the solution using filter methods the relations between stiffness overestimation the analysis system and the applied length scale are examined while a high resolution topology is maintained the computational cost associated with nested topology optimization is reduced significantly compared with the use of first order finite elements this reduction is caused by exploiting the decoupling of density and analysis mesh and by condensing the higher order modes out of the stiffness matrix

robust exponential convergence of hp fem in balanced norms for singularly perturbed reaction diffusion problems corner domains abstract the h p version of the finite element method is applied to singularly perturbed reaction diffusion type equations on polygonal domains the solution exhibits boundary layers as well as corner layers on a class of meshes that are suitably refined near the boundary and the corners robust exponential convergence in the polynomial degree is shown in both a balanced norm and the maximum norm

a straightforward structure to construct shape functions for variable p order meshes this paper describes a method for specifying variable p order meshes based on the topological hierarchy of mesh entities defining the finite elements a decomposition of p version mesh entity shape functions into a product of a function defined over the mesh entity and a blending function defined over the elements that the mesh entity bounds is presented the decomposed shape functions allow the effective construction of the shape functions and derivatives needed to construct element matrices for variable p enrichment

sharp endpoint l p lp estimates for schrodinger groups let l be a non negative self adjoint operator acting on l 2 x where x is a space of homogeneous type with a dimension n suppose that the heat operator e tl satisfies the generalized gaussian p 0 p 0 estimates of order m for some 1 le p 0 2 in this paper we prove sharp endpoint l p sobolev bound for the schrodinger group e itl that is for every p in p 0 p 0 there exists a constant c c n p 0 independent of t such that begin aligned left i l s e itl f right p le c 1 t s vert f vert p quad t in mathbb r quad s ge n big 1 over 2 1 over p big end aligned as a consequence the above estimate holds for all 1 p infty when the heat kernel of l satisfies a gaussian upper bound this extends classical results due to feffermann and stein and miyachi for the laplacian on the euclidean spaces mathbb r n we also give an application to obtain an endpoint estimate for l p boundedness of the riesz means of the solutions of the schrodinger equations

roof duality complementation and persistency in quadratic 0 1 optimization the paper is concerned with the primal problem of maximizing a given quadratic pseudo boolean function four equivalent problems are discussed the primal the complementation the discrete rhys lp and the weighted stability problem of a sam graph each of them has a relaxation the roof dual the quadratic complementation the continuous rhys lp and the fractional weighted stability problem of a sam graph the main result is that the four gaps associated with the four relaxations are equal furthermore a solution to any of these problems leads at once to solutions of the other three equivalent ones the four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem the optimal solutions of the roof dual define best linear majorantsp x off having the following persistency property if theith coefficient inp is positive negative thenx i 1 0 in every optimum of the primal problem several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal on the other hand a class of gap free functions properly including the supermodular ones is exhibited

optimal shape design for thin walled beam cross sections problems of shape optimization for thin walled beam cross sections are investigated in particular shape optimization under torsional loading is treated the shape of the beam cross section is described by non uniform rational b splines nurbs biquadratic and p version finite elements are used to calculate the warping function the definition of the element geometry is carried out by isoparametric and b spline mappings both methods are discussed and compared for structural shape optimization the b spline mapping in connection with the p version finite elements is very efficient the optimization is implemented using convex linearisation and a dual method of mathematical programming sensitivity analysis is performed analytically sample calculations are included

comparison of various orthogonal polynomials in hp version time finite element method four types of orthogonal polynomials legendre chebyshev hermite and integrated legendre are evaluated as basis functions in the time finite element method to solve initial value problems governed by second order differential equations condition numbers of the augmented stiffness matrix for the selected problems are estimated by increasing the number of polynomial terms in the expansion results for the cpu time using an ibm 3090 300e vf computer and the estimated condition numbers using imsl subroutine dlfcrg for each of four basis functions are presented the augmented stiffness matrix for the case of integrated legendre polynomials is found to have the best condition number behavior and that for the hermite polynomial the worst the integrated legendre polynomials require the most cpu time whereas the chebyshev polynomials require the least

solving quadratic 0 1 problems by semidefinite programs and cutting planes we present computational experiments for solving quadratic 0 1 problems our approach combines a semidefinite relaxation with a cutting plane technique and is applied in a branch and bound setting our experiments indicate that this type of approach is very robust and allows to solve many moderately sized problems having say less than 100 binary variables in a routine manner 1998 the mathematical programming society inc published by elsevier science b v

numerical analysis of dissolution processes in cementitious materials using discontinuous and continuous galerkin time integration schemes the present paper is concerned with the numerical integration of non linear reaction diffusion problems by means of discontinuous and continuous galerkin methods the first order semidiscrete initial value problem of calcium leaching of cementitious materials based on a phenomenological dissolution model an electrolyte diffusion model and the spatial p finite element discretization is used as a highly non linear model problem a p finite element method is used for the spatial discretization in the context of discontinuous galerkin methods the semidiscrete mass balance and the continuity of the primary variables are weakly formulated within time steps and between time steps respectively continuous galerkin methods are obtained by the strong enforcement of the continuity condition as special cases the introduction of a natural time co ordinate allows for the application of standard higher order temporal shape functions of the p lagrange type and the well known gauss legendre quadrature of associated time integrals it is shown that arbitrary order accurate integration schemes can be developed within the framework of the proposed temporal p galerkin methods selected benchmark analyses of calcium dissolution demonstrate the robustness of these methods with respect to pronounced changes of the reaction term and non smooth changes of dirichlet boundary conditions copyright 2006 john wiley sons ltd

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

hierarchal triangular elements using orthogonal polynomials hierarchal elements are finite elements which have the useful property that elements with different polynomial orders can be used together in the same mesh without causing discontinuities this paper introduces a new hierarchal triangular element in which the basis functions are constructed from orthogonal polynomials jacobi polynomials the resulting element is shown to be better conditioned than the earlier hierarchal element of rossow and katz 1 recursive formulas allow the complete set of basis functions for an element to be efficiently evaluated at a given point in addition the formulas can be used to generate pre computed universal matrices examples are given of universal matrices up to order 4 for the generalized helmholtz equation an electromagnetic problem involving a length of transmission line is used to show the usefulness of the new elements

the approximation of solutions of elliptic boundary value problems via the p version of the finite element method the approximation theory developed in 11 is used to determine the piecewise polynomial approximability of solutions of elliptic problems on polygonal domains in mathbb r 2 and polyhedra in mathbb r 3 from these estimates convergence orders for the p version of the finite element method applied to such problems are readily obtained the critical issue is the approximation of the singularities which occur at the nonsmooth parts of the domain boundaries it is seen that the estimates of 11 involving the weighted sobolev spaces z l s are well suited for treating such singular functions yielding directly the optimal approximation degree up to an arbitrarily small varepsilon numerical results for two problems from two dimensional linear elasticity are also presented the computations show that the predicted order of convergence is achieved even for low values of p moreover in contrast to the usual h version of the finite element method the point at which the p version enters the asym

one pass heuristics for large scale unconstrained binary quadratic problems abstract many significant advances have been made in recent years for solving unconstrained binary quadratic programs uqp as a result the size of problem instances that can be efficiently solved has grown from a hundred or so variables a few years ago to 2000 or 3000 variables today these advances have motivated new applications of the model which in turn have created the need to solve even larger problems in response to this need we introduce several new one pass heuristics for solving very large versions of this problem our computational experience on problems of up to 9000 variables indicates that these methods are both efficient and effective for very large problems the significance of problems of this size is that they not only open the door to solving a much wider array of real world problems but also that the standard linear mixed integer formulations of the nonlinear models involve over 40 000 000 variables and three times that many constraints our approaches can be used as stand alone solution methods or they can serve as procedures for quickly generating high quality starting points for other more sophisticated methods

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

computational error estimates and adaptive processes for some nonlinear structural problems abstract in earlier papers the authors introduced and analyzed the calculation of reliable a posteriori error estimates for finite element solutions and discussed the design and effectivity of adaptive procedures based upon them while most of this work concerned linear problems this paper is intended to show that the same approaches remain also highly effective in the nonlinear case as a model problem a planar elastic rod is considered involving both material as well as geometrical nonlinearities but as far as possible the discussion is kept general for nonlinear problems of this type interest centers on an analysis of the shape and features of the equilibrium surface after some general remarks about such surfaces and the related computational problems a general continuation process is summarized and some of its extensions for determining limit points and tracing stability paths are discussed then estimators are introduced for the error along the solution paths and of the computed critical values experimental results for the model problem show the effectivity of these estimators and of the adaptive procedures based upon them then some aspects relating to the occurrence and identification of spurious solutions are discussed in order to illustrate desirable generalizations of these results the paper ends with an outline of some results for linear problems of the type that should be achievable also in the nonlinear case

estimates for schrodinger evolution equations on demontre que pour des donnees de cauchy dans l 1 r n la solution d une equation d evolution de schrodinger a coefficients constants d ordre 2m est uniformement bornee pour t 0 de borne 1 t c ou c est un entier c n 2m 1

a distortion measure to validate and generate curved high order meshes on cad surfaces with independence of parameterization the first author was sponsored by cur from diue of the generalitat de catalunya and the european social fund grants fi dgr 11 and be dgr 12 and by the ferran sunyer i balaguer foundation grant fsb 13 the work of the corresponding author was partially supported by the boeing co us air force office of scientific research european commission through the boeing mit alliance the computational math program marie sklodowska curie actions hipermegaflows individual fellowship grant

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

bounds for decoupled design and analysis discretizations in topology optimization summary topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution this paper discusses the relation between the number of design variables per element and the order of the elements used for analysis we derive that beyond a maximum number of design variables certain sets of material distributions cannot be discriminated based on the corresponding analysis results this makes the design description inefficient and the solution of the optimization problem non unique to prevent this we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non uniqueness copyright 2016 the authors international journal for numerical methods in engineering published by john wiley sons ltd

automated adaptive two dimensional system for the hp version of the finite element method this paper presents an automated adaptive finite element modelling system based on the hp version of the finite element method error estimation and correction indication procedures with an automatic mesh generator and a p version analysis code are combined to provide a computationally efficient modelling environment error prediction techniques are employed to find the best combination of finite element discretization h and overall polynomial order p needed to achieve the prescribed level of accuracy the automated adaptive modelling results demonstrate the capability of the modelling system of predicting discretizations to perform a p version finite element analysis to achieve prescribed levels of accuracy in the most efficient manner

efficient reduction of polynomial zero one optimization to the quadratic case we address the problem of optimizing a polynomial with real coefficients over binary variables we show that a complete polyhedral description of the linearization of such a problem can be derived in a simple way from the polyhedral description of the linearization of some quadratic optimization problem the number of variables in the latter linearization is only slightly larger than in the former if polynomial constraints are present in the original problem then their linearized counterparts carry over to the linearized quadratic problem unchanged if the original problem formulation does not contain any constraints we obtain a reduction to unconstrained quadratic zero one optimization which is equivalent to the well studied max cut problem the separation problem for general unconstrained polynomial zero one optimization thus reduces to the separation problem for the cut polytope this allows us to transfer the entire knowledge gained for the latter polytope by intensive research and in particular the sophisticated separation techniques that have been developed we report preliminary experimental results obtained with a straightforward implementation of this approach

plancherel type estimates and sharp spectral multipliers abstract we study general spectral multiplier theorems for self adjoint positive definite operators on l2 x where x is any open subset of a space of homogeneous type we show that the sharp hormander type spectral multiplier theorems follow from the appropriate estimates of the l2 norm of the kernel of spectral multipliers and the gaussian bounds for the corresponding heat kernel the sharp hormander type spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the riesz means summability which we also study here we discuss several examples which include sharp spectral multiplier theorems for a class of scattering operators on r3 and new spectral multiplier theorems for the laguerre and hermite expansions

analytic regularity of stokes flow on polygonal domains in countably weighted sobolev spaces we investigate the analytic regularity of the stokes problem in a polygonal domain r2 with straight sides and piecewise analytic data we establish a shift theorem in weighted sobolev spaces of arbitrary order with explicit control of the order dependence of the constants the shift theorem in the framework of countably weighted sobolev spaces implies in particular interior analyticity and gevrey type analytic regularity near the corners

quadratic reformulations of nonlinear binary optimization problems very large nonlinear unconstrained binary optimization problems arise in a broad array of applications several exact or heuristic techniques have proved quite successful for solving many of these problems when the objective function is a quadratic polynomial however no similarly efficient methods are available for the higher degree case since high degree objectives are becoming increasingly important in certain application areas such as computer vision various techniques have been recently developed to reduce the general case to the quadratic one at the cost of increasing the number of variables by introducing additional auxiliary variables in this paper we initiate a systematic study of these quadratization approaches we provide tight lower and upper bounds on the number of auxiliary variables needed in the worst case for general objective functions for bounded degree functions and for a restricted class of quadratizations our upper bounds are constructive thus yielding new quadratization procedures finally we completely characterize all minimal quadratizations of negative monomials

sharp spectral multipliers for operators satisfying generalized gaussian estimates abstract let l be a non negative self adjoint operator acting on l 2 x where x is a space of homogeneous type assume that l generates a holomorphic semigroup e t l which satisfies generalized m th order gaussian estimates in this article we study singular and dyadically supported spectral multipliers for abstract self adjoint operators we show that in this setting sharp spectral multiplier results follow from plancherel or stein tomas type estimates these results are applicable to spectral multipliers for a large class of operators including m th order elliptic differential operators with constant coefficients biharmonic operators with rough potentials and laplace type operators acting on fractals

transformation of general binary mrf minimization to the first order case we introduce a transformation of general higher order markov random field with binary labels into a first order one that has the same minima as the original moreover we formalize a framework for approximately minimizing higher order multilabel mrf energies that combines the new reduction with the fusion move and qpbo algorithms while many computer vision problems today are formulated as energy minimization problems they have mostly been limited to using first order energies which consist of unary and pairwise clique potentials with a few exceptions that consider triples this is because of the lack of efficient algorithms to optimize energies with higher order interactions our algorithm challenges this restriction that limits the representational power of the models so that higher order energies can be used to capture the rich statistics of natural scenes we also show that some minimization methods can be considered special cases of the present framework as well as comparing the new method experimentally with other such techniques

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

new function spaces of bmo type the john nirenberg inequality interpolation and applications in this paper we introduce and develop some new function spaces of bmo bounded mean oscillation type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type the new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity and they generalize the classical bmo space we show that the john nirenberg inequality holds on these spaces and they interpolate with lp spaces by the complex interpolation method we then give applications on lp boundedness of singular integrals whose kernels do not satisfy the hormander condition 2005 wiley periodicals inc

improved bounds for stein s square functions supported in part by nrf grant 2009 0072531 korea micinn grant mtm2010 16518 spain erc grant 277778 europe and nsf grant 0652890 usa

aspects of an adaptive hp finite element method adaptive strategy conforming approximation and efficient solvers the main components needed for an adaptive hp version finite element algorithm are discussed an adaptive hp refinement strategy effective methods for constructing conforming hp approximations and efficient solvers for the large ill conditioned systems of linear equations together these provide the methodology for an effective adaptive hp version algorithm the presentation emphasizes the links between the differing components showing how the algorithms may be implemented efficiently in practice the main principles are illustrated by use of concrete examples so that a non expert may develop their own adaptive hp code the performance of the whole algorithm is illustrated for some representative problems taken from linear elasticity

an adaptive mesh refinement strategy for finite element solution of the elliptic problem abstract in this paper we develop an adaptive finite element method for elliptic problems first we assume that in each subdomain the norm of the approximation error at the current mesh configuration is bounded by the norm of the approximation error obtained at the previous mesh configuration for some norm h s then an a posteriori error estimator is designed based on the approximate solution correction between the solution on the last two mesh configurations based on this new error estimator the element wise refinement strategy in each subdomain is provided for a given tolerance a discussion on the choice of the coefficients in the assumption is given for different norm spaces and for different degrees of finite element family four 2d numerical benchmark examples of different domains and two 3d numerical benchmark examples are tested to demonstrate the robustness of our method when possible our numerical results are also compared to corresponding results from existing methods all the results show that the proposed method is robust and efficient in terms of the number of degrees of freedom

an analysis of thep version of the finite element method for nearly incompressible materials in this paper we analyze the behavior of the so calledp version of the finite element method when applied to the equations of plane strain linear elasticity we establish optimal rate error estimates that are uniformly valid independent of the value of the poisson ratio v in the interval 0 1 2 this shows that thep versiondoes not exhibit the degeneracy phenomenon which has led to the use of various only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material

an estimate of the babuska brezzi inf sup discrete stability constant for general linear petrov galerkin finite element formulations an estimate of the babuska brezzi stability constant an a priori lower bound estimate of the babuska brezzi bb inf sup discrete stability constant is given for general linear petrov galerkin formulations the estimate is based on reasonable assumptions regarding a specific auxiliary adjoint problem the similarities and discrepancies of the presented method compared to the well known fortin s criterion are also noted the estimate may be used to obtain numerical verification of the bb condition under the assumption that the finite element basis functions are almost orthogonal

the weighted finite element method for elasticity equations on unbounded domains abstract by introducing the weighted riesz galerkin method with a special weight function oh jou 23 made it possible to apply mam the method of auxiliary mapping introduced by babuska oh to general elliptic boundary value problems on unbounded domains in this paper this method is further generalized to yield highly accurate approximate solutions for linear elasticity problems on unbounded domains with bounded or unbounded boundaries it is shown that in the framework of the p version of the fem this method does efficiently handle elasticity problems on unbounded domains and yields accurate solutions at low cost

higher order finite elements based on generalized eigenfunctions of the laplacian we present a new class of higher order finite elements based on generalized eigenfunctions of the laplace operator which are suitable for both product and simplicial geometries in d due to simultaneous orthogonality of the generalized eigenfunctions under both the h and l2 products and their almost negligible dependence on reference maps such finite elements are an excellent choice for the discretization of second order elliptic problems by the hp fem analysis is illustrated by numerical results and comparisons with other popular higher order finite elements are presented the new elements are used to compute efficiently the model of an electrostatic micromotor copyright 2007 john wiley sons ltd

adaptive solution strategy for solving large systems of p type finite element equations a solution strategy is proposed and implemented for taking advantage of the hierarchical structure of linear equation sets arising from the p type finite element method using a hierarchical basis function set the algorithm dynamically branches to either direct or iterative solution methods in the iterative solution branch the substructure of the finite element equation set is used to generate a lower order preconditioner for a preconditioned conjugate gradient pcg method the convergence rate of the pcg algorithm is monitored to improve the heuristics used in the choice of the preconditioner the robustness and efficiency of the method are demonstrated on a variety of three dimensional examples utilizing both hexahedral and tetrahedral mesh discretizations this strategy has been implemented in a p version finite element code which has been used in an industrial environment for over two years to solve mechanical design problems

from finite differences to finite elements a short history of numerical analysis of partial differential equations abstract this is an account of the history of numerical analysis of partial differential equations starting with the 1928 paper of courant friedrichs and lewy and proceeding with the development of first finite difference and then finite element methods the emphasis is on mathematical aspects such as stability and convergence analysis