Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 1: 177 - 202

DOI: https://doi.org/10.1007/s11464-010-0084-7

RESEARCH ARTICLE

Sharp a posteriori error estimate for elliptic equation with singular data

  • Gang YUAN ,
  • Ruo LI
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  • School of Mathematical Science, Peking University, Beijing 100871, China

Received date: 02 Apr 2010

Accepted date: 06 Sep 2010

Published date: 01 Feb 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We introduce two residual type a posteriori error estimators for second-order elliptic partial differential equations with its right-hand side in Lp (1<p≤2) space. Both estimators are proved to yield global upper and local lower bounds for the W1,p seminorm of the error. We adopt the estimators as the indicators in h-mesh adaptive method to solve two typical model problems. It is verified by the numerical results that the estimators lead to optimal orders of convergence.

Key words： Lp space; finite element method; adaptive mesh refinement; a posteriori error estimate

Cite this article

Gang YUAN , Ruo LI . Sharp a posteriori error estimate for elliptic equation with singular data[J]. Frontiers of Mathematics in China, 2011 , 6(1) : 177 -202 . DOI: 10.1007/s11464-010-0084-7

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