A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem

被引：7
|
作者：
Deng, Yanling [1 ]
Wang, Fei [1 ]
Wei, Huayi [2 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
[2] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2020年 / 83卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Elliptic variational inequality; A posteriori error analysis; Virtual element method; Adaptive mesh refinement; Polygonal meshes; DISCONTINUOUS GALERKIN METHODS; ELLIPTIC VARIATIONAL-INEQUALITIES; FORMULATION; EFFICIENT;
D O I：
10.1007/s10915-020-01242-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a posteriori error analysis of the virtual element method (VEM) for a simplified friction problem, which is a representative elliptic variational inequality of the second kind. By treating hanging nodes as vertices of polygonal elements, the virtual element method does not require any local mesh post-processing after the adaptive mesh refinement. In this work, residual type error estimators are derived for designing adaptive VEM to solve the simplified friction problem. Furthermore, the reliability and efficiency of the error estimators are proved. Finally, a numerical example is given to verify the theoretical results.
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页数：20
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