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

S. Prudhomme; F. Nobile; L. Chamoin; J. T. Oden

doi:10.1002/num.10082

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

S. Prudhomme, F. Nobile, L. Chamoin, J. T. Oden^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 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 language	English (US)
Pages (from-to)	165-192
Number of pages	28
Journal	Numerical Methods for Partial Differential Equations
Volume	20
Issue number	2
DOIs	https://doi.org/10.1002/num.10082
State	Published - Mar 2004
Externally published	Yes

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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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.",

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AU - Nobile, F.

AU - Chamoin, L.

AU - Oden, J. T.

PY - 2004/3

Y1 - 2004/3

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AB - 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.

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

Abstract

ASJC Scopus subject areas

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