Analysis of a Subdomain-based Error Estimator for Finite Element Approximations of Elliptic Problems

Serge Prudhomme, F. Nobile, L. Chamoin, J. T. Oden*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

In this article we analyze a subdomain residual error estimator for finite element approximations of elliptic problems. It is obtained by solving local problems on patches of elements in weighted spaces and provides an upper bound on the energy norm of the error when the local problems are solved in sufficiently enriched discrete spaces. A guaranteed lower bound on the error is also derived by a simple postprocess of the solutions to the local problems. Numerical tests show very good effectivity indices for both the upper and lower bounds and a strong reliability of this estimator even for coarse meshes.

Original languageEnglish (US)
Pages (from-to)165-192
Number of pages28
JournalNumerical Methods for Partial Differential Equations
Volume20
Issue number2
DOIs
StatePublished - Jan 1 2004

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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