ANISOTROPIC ERROR ESTIMATES OF THE LINEAR NONCONFORMING VIRTUAL ELEMENT METHODS

被引：28

作者：

Cao, Shuhao ^{[1
]}

Chen, Long ^{[1
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2019年 / 57卷 / 03期

基金：

美国国家科学基金会;

关键词：

virtual element methods; polytopal finite elements; anisotropic error analysis; nonconforming method; ORDER; EQUATIONS; MESHES;

D O I：

10.1137/18M1196455

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A refined a priori error analysis of the lowest-order (linear) nonconforming virtual element method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on the shape regularity of polytopal meshes. A new error equation for the lowest-order (linear) nonconforming VEM is derived for any choice of stabilization, and a new stabilization using a projection on an extended element patch is introduced for the error analysis on anisotropic elements.

引用

页码：1058 / 1081

页数：24

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