Analysis of a subdomain-based error estimator for finite element approximations of elliptic problems

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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Numerical Methods for Partial Differential Equations, Wiley, 2004, 20 (2), pp.165-192. 〈10.1002/num.10082〉
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https://hal.archives-ouvertes.fr/hal-01580948
Contributeur : Ludovic Chamoin <>
Soumis le : dimanche 3 septembre 2017 - 23:44:32
Dernière modification le : mardi 11 décembre 2018 - 01:21:37

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Serge Prudhomme, Fabio Nobile, Ludovic Chamoin, J. Tinsley Oden. Analysis of a subdomain-based error estimator for finite element approximations of elliptic problems. Numerical Methods for Partial Differential Equations, Wiley, 2004, 20 (2), pp.165-192. 〈10.1002/num.10082〉. 〈hal-01580948〉

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