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
收藏
页码：1058 / 1081
页数：24
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