NODAL O(h4)-SUPERCONVERGENCE IN 3D BY AVERAGING PIECEWISE LINEAR, BILINEAR, AND TRILINEAR FE APPROXIMATIONS

被引：14

作者：

Hannukainen, Antti ^{[1
]}

Korotov, Sergey ^{[2
]}

Krizek, Michal ^{[3
]}

机构：

[1] Helsinki Univ Technol, Inst Math, FIN-02015 Espoo, Finland

[2] Tampere Univ Technol, Dept Math, FI-33101 Tampere, Finland

[3] Acad Sci Czech Republic, Inst Math, CZ-11567 Prague 1, Czech Republic

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2010年 / 28卷 / 01期

基金：

芬兰科学院;

关键词：

Higher order error estimates; Tetrahedral and prismatic elements; Superconvergence; Averaging operators; MONOMIAL CUBATURE RULES; FINITE-ELEMENT METHODS; SIMPLICIAL PARTITIONS; SUPERCONVERGENCE; COMPILATION; STROUD; MESHES;

D O I：

10.4208/jcm.2009.09-m1004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct and analyse a nodal O(h(4))-superconvergent FE scheme for approximating the Poisson equation with homogeneous boundary conditions in three-dimensional domains by means of piecewise trilinear functions. The scheme is based on averaging the equations that arise from FE approximations on uniform cubic, tetrahedral, and prismatic partitions. This approach presents a three-dimensional generalization of a two-dimensional averaging of linear and bilinear elements which also exhibits nodal O(h(4))-superconvergence (ultraconvergence). The obtained superconvergence result is illustrated by two numerical examples.

引用

页码：1 / 10

页数：10

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