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Analysis of a subdomain‐based error estimator for finite element approximations of elliptic problems
Author(s) -
Prudhomme S.,
Nobile F.,
Chamoin L.,
Oden J. T.
Publication year - 2004
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10082
Subject(s) - estimator , finite element method , polygon mesh , mathematics , upper and lower bounds , norm (philosophy) , residual , approximations of π , method of mean weighted residuals , mathematical optimization , mathematical analysis , algorithm , geometry , statistics , physics , political science , law , thermodynamics , galerkin method
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. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 165–192, 2004