ERROR ANALYSIS AND GLOBAL SUPERCONVERGENCES FOR THE SIGNORINI PROBLEM WITH LAGRANGE MULTIPLIER METHODS

1. IntroductionIt is well known that contact problems have always occupied a position of special importancein the mechanics of solids. So it attracted particular attention of engineers and computationalexperts. In the last ten years, with the development …     

Interior estimates for nonconforming finite element methods

Summary. Interior error estimates are derived for a wide class of nonconforming finite element methods for second order scalar elliptic boundary value problems. It is shown that the error in an interior domain can be estimated by three terms: the first one measures the local approximability of the finite element space to the exact solution, the second one measures the degree of continuity of the finite element space (the consistency error), and the last one expresses the global effect through the error in an arbitrarily weak Sobolev norm over a slightly larger domain. As an application, interior superconvergences of some difference quotients of the finite element solution are obtained for the derivatives of the exact solution when the mesh satisfies some translation invariant condition. Received December 29, 1994     

Biquadratic finite volume element methods based on optimal stress points for parabolic problems

In this paper, the semi-discrete and full discrete biquadratic finite volume element schemes based on optimal stress points for a class of parabolic problems are presented. Optimal order error estimates in H¹ and L² norms are derived. In addition, the superconvergences of numerical gradients at optimal stress points are also discussed. A numerical experiment confirms some results of theoretical analysis.     

CASCADIC MULTIGRID METHODS FOR MORTAR WILSON FINITE ELEMENT METHODS ON PLANAR LINEAR ELASTICITY

Cascadic multigrid technique for mortar Wilson finite element method of homogeneous boundary value planar linear elasticity is described and analyzed. First the mortar Wilson finite element method for planar linear elasticity will be analyzed, and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigrid method for the mortar finite element discrete problem is described. Suitable grid transfer operator and smoother are developed which lead to an optimal cascadic multigrid method. Finally, the computational results are presented.     

Wilson元特征值下逼近准确特征值

该文讨论矩形域上Laplace算子特征值问题有限元近似.证明了Wilson非协调有限元特征值下逼近准确特征值,从而解决了有限元法中长期存在的一个猜想.     

V-cycle multigrid methods for Wilson nonconforming element

Here two types of optimal V-cycle multigrid algorithms are presented for Wilson nonconforming finite element.     

High accuracy analysis of elliptic eigenvalue problem for the Wilson nonconforming finite element

1. IntroductionLet fi be a unit sqllare domain in the ac-plane and Th = {eij}:j71 be a rectangularpartition of the domain .fi, where us m are two positive illtegers, eij ~ [xi-1 ) xi] x [yi-1, yi]are rectagular elements, and0~ xo < al < ..' < xu = 1, 0 = yo < yi < ... < ac = 1are two one-dimensional partitions on the x-axis and yials, respectively. Define hi =xi - fi-h hi = yi - ie-l, and the mesh size h = ma-c{hi, hi}::,. As usual, Th is said tobe quasi-uniform if there exists a constant c s…     

Anisotropic Superconvergence Analysis for the Wilson Nonconforming Element

1 Introduction The Wilson nonconforming element has been widely used in computational mechanics and struc- tural engineering because of its good convergence. In many practical cases, it seems better than the bilinear conforming finite element. This phenomenon causes the great interest of many people who study finite elements. Some papers about the Wilson element have been published which deal with superconvergence. In [6], the superclose property and the global superconvergence are obtained …     

各向异性网格下Wilson元的超收敛性分析

在各向异性网格下研究了二阶椭圆边值问题的Wilson有限元方法,利用单元构造的特殊性和一些新的技巧得到相应的超逼近和超收敛结果.数值算例的结果与理论分析是相吻合的.     

轴对称问题的Wilson四边形单元

给出了一族轴对称问题的改进Ｗｉｌｓｏｎ元，利用强分片检验证明了其收敛性，讨论了单元函数结构·从而给出了一种构造收敛的轴对称非协调元方法·     

A new superconvergence property of Wilson nonconforming finite element

Summary. In this paper the Wilson nonconforming finite element method is considered to solve a class of two-dimensional second-order elliptic boundary value problems. A new superconvergence property at the vertices and the midpoints of four edges of rectangular meshes is obtained. Received May 5, 1995 / Revised version received November 11, 1996     

THE MULTIGRID METHOD OF WILSONELEMENT ON ARBITRARYQUADRILATERAL MESHES WITH TWONEW VARIATIONAL FORMULATIONS

1.IntroductionShiZhongci[']hasshownthattheWilsonelementonarbitraryquadrilateralmesheswasconvergelltunderacertainconditionwithoutmodificationsofthevariationalformulation.P.LesaintandM.Zlamal[2]gaveamathematicalanalysisoftheconvergenceofthemodifiedWilsonelemeflt.Withtheseideas,thispapergivestwosimplevariationalformulationsforthequadrilateralWilsonelementandshowstheirconvergencewiththenewvariationalformulations.Usingthenewvariationalformulations,wecanreduceourcomputationalcostsbecausetwotermsa…     

Superconvergence analysis and error expansion for the Wilson nonconforming finite element

Summary. In this paper the Wilson nonconforming finite element is considered for solving a class of two-dimensional second-order elliptic boundary value problems. Superconvergence estimates and error expansions are obtained for both uniform and non-uniform rectangular meshes. A new lower bound of the error shows that the usual error estimates are optimal. Finally a discussion on the error behaviour in negative norms shows that there is generally no improvement in the order by going to weaker norms. Received July 5, 1993     

Convergence of the nonconforming Wilson element for arbitrary quadrilateral meshes

Summary A modified variational formulation, recently introduced by Taylor, Beresford and Wilson for solving second order problems, using the nonconforming Wilson element is here analysed. It is shown that the Patch Test is satisfied and that stresses and displacements are respectively first and second order accurate for arbitrary quadrilateral meshes.     

Mesh optimization for singular axisymmetric harmonic maps from the disc into the sphere

We describe in a mathematical setting the singular energy minimizing axisymmetric harmonic maps from the unit disc into the unit sphere; then, we use this as a test case to compute optimal meshes in presence of sharp boundary layers. For the well-posedness of the continuous minimizing problem, we introduce a lower semicontinuous extension of the energy with respect to weak convergence in BV, and we prove that the extended minimization problem has a unique singular solution. We then show how a moving finite element method, in which the mesh is an unknown of the discrete minimization problem obtained by finite element discretization, mimics this geometric point of view. Finally, we present numerical computations with boundary layers of zero thickness, and we give numerical evidence of the convergence of the method. This last aspect is proved in another paper. This work was supported by the Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan, 61 av. du Président Wilson, 94235 Cachan Cedex, France     

非正则条件下类Wilson元的构造及其应用

本文在非正则性条件下，研究了窄四边形上的类Wilson元。通过参考元上类Wilson元的构造，证明了由此产生的有限元对任意窄四边形剖分通过Irons分片检查，得到了二阶问题的误差估计。结果表明，该单元的收敛性质与Wilson元的类似。     

Sobolev型方程高次Wilson元逼近及超收敛分析

In this paper,a new higher order Wilson element is presented,and the convergence is proved.Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.     

一类六参数非协调任意凸四边形单元

本文构造了一类六参数非协调四边形单元,证明由此产生的有限元对任意四边形网格通过Irons分片检查,其收敛效果同Wilson元相当且形状函数的选择不依赖于单元本身。类Wilson元及改进的Wilson任意四边形单元是其中的特例。     

关于非协调位移元与杂交应力元的对应性

本文阐明了E.L.Wilson[3]等的非协调移位元与卞学鐄的杂交应力元之间所存在的对应性.     

ACCURACY ANALYSIS FOR QUASI-WILSON ELEMENT

1IntroductionItiswellknownthattheconvergencebehaviorofthehausnonconformingWilsonel-ementismuchbetterthanofconforndllgbilinearelement,soWilsonelementiswidelyu8edinengineeringcomputation.ButWilsonelementisonlyconvergentforrectangularandpar-allelograxnmeshes.Inordertoextendthiselementtoarbitraryquadrilateralmeshes,variousimProvedWilsonelementsweredeveloped,suchasQP6element,generalizedisoparanletricelement,isoparametricQuasiconformingelement,andsoon(see[1-3]).However,the8hapefunctionsofallthes…