Local a Posteriori Error Estimates and Adaptive Control of Pollution Effects

Numer. Methods PDE, 19 (2003), 421-442.

Xiaohai Liao
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA

xxl@math.umd.edu

Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA

rhn@math.umd.edu

Abstract

Local a posteriori error estimators are derived for linear elliptic problems over general polygonal domains in $2d$. The estimators lead to a sharp upper bound for the energy error in a local region of interest. This upper bound consists of $H^1$-type local error indicators in a slightly larger subdomain, plus weighted $L^2$-type local error indicators outside this subdomain which account for the pollution effects. This constitutes the basis of a local adaptive refinement procedure. Numerical experiments show a superior performance than the standard global procedure as well as the generation of locally quasi-optimal meshes.