Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems

被引：11

作者：

Cai, Difeng ^{[1
]}

Cai, Zhiqiang ^{[2
]}

Zhang, Shun ^{[3
]}

机构：

[1] Emory Univ, Dept Math, 201 Dowman Dr, Atlanta, GA 30322 USA

[2] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

[3] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

来源：

NUMERISCHE MATHEMATIK | 2020年 / 144卷 / 01期

基金：

美国国家科学基金会;

关键词：

65N15; 65N30; 65N50; ELLIPTIC-EQUATIONS; RECOVERY;

D O I：

10.1007/s00211-019-01075-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a patch-based equilibrated flux recovery procedure for the conforming finite element approximation to diffusion problems. The recovered flux is computed as the solution to a local constraint-free minimization problem on each patch. The approach is valid for higher order conforming elements in both two and three dimensions. The resulting estimator admits guaranteed reliability and the robust local efficiency is proved under the quasi-monotonicity condition of the diffusion coefficient. Numerical experiments are given to confirm the theoretical results.

引用

页码：1 / 21

页数：21

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