POINTWISE A POSTERIORI ERROR CONTROL FOR DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS

被引：20

作者：

Demlow, Alan ^{[1
]}

Georgoulis, Emmanuil H. ^{[2
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

[2] Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2012年 / 50卷 / 05期

基金：

美国国家科学基金会;

关键词：

pointwise a posteriori error estimate; discontinuous Galerkin method; elliptic problem; adaptive algorithm; FINITE-ELEMENT-METHOD; MAXIMUM NORM; APPROXIMATION; CONVERGENCE; ESTIMATORS; MATRICES; SYSTEMS;

D O I：

10.1137/110846397

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An a posteriori error bound for the maximum (pointwise) error for the interior penalty discontinuous Galerkin method for a standard elliptic model problem on polyhedral domains is presented. The computational domain is not required to be Lipschitz, thus allowing for domains with cracks and other irregular polyhedral domains. The proof is based on the direct use of Green's functions and varies substantially from the approach used in previous proofs of similar L-infinity estimates for (continuous) finite element methods in the literature. Numerical experiments indicating the good behavior of the resulting a posteriori bounds within an adaptive algorithm are also presented.

引用

页码：2159 / 2181

页数：23

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