ROBUST EQUILIBRATED RESIDUAL ERROR ESTIMATOR FOR DIFFUSION PROBLEMS: CONFORMING ELEMENTS

被引：29

作者：

Cai, Zhiqiang ^{[1
]}

Zhang, Shun ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2012年 / 50卷 / 01期

基金：

美国国家科学基金会;

关键词：

a posteriori error estimator; equilibrated residual error estimator; finite element; ELLIPTIC-EQUATIONS; RECOVERY; BOUNDS;

D O I：

10.1137/100803857

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper analyzes an equilibrated residual a posteriori error estimator for the diffusion problem. The estimator, which is a modification of those in [D. Braess and J. Schoberl, Math. Comput., 77 (2008), pp. 651-672; R. Verfurth, SIAM J. Numer. Anal., 47 (2009), pp. 3180-3194], is based on the Prager-Synge identity and on a local recovery of an equilibrated flux. Numerical results for an interface test problem show that the modification is necessary for the robustness of the estimator. When the distribution of diffusion coefficients is local quasi-monotone, it is shown theoretically that the estimator is robust with respect to the size of jumps.

引用

页码：151 / 170

页数：20

共 31 条

[1] A UNIFIED APPROACH TO A POSTERIORI ERROR ESTIMATION USING ELEMENT RESIDUAL METHODS [J].