A posteriori error estimators for mixed approximations of eigenvalue problems

In this paper we introduce and analyze an a posteriori error estimator for the approximation of the eigenvalues and eigenvectors of a second-order elliptic problem obtained by the mixed finite element method of Raviart-Thomas of the lowest order. We define an error estimator of the residual type whi...

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Publicado: 1999
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v9_n8_p1165_Duran
http://hdl.handle.net/20.500.12110/paper_02182025_v9_n8_p1165_Duran
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02182025_v9_n8_p1165_Duran
record_format dspace
spelling paper:paper_02182025_v9_n8_p1165_Duran2023-06-08T15:21:23Z A posteriori error estimators for mixed approximations of eigenvalue problems In this paper we introduce and analyze an a posteriori error estimator for the approximation of the eigenvalues and eigenvectors of a second-order elliptic problem obtained by the mixed finite element method of Raviart-Thomas of the lowest order. We define an error estimator of the residual type which can be computed locally from the approximate eigenvector and prove that the estimator is equivalent to the norm of the error in the approximation of the eigenvector up to higher order terms. The constants involved in this equivalence depend on the corresponding eigenvalue but are independent of the mesh size, provided the meshes satisfy the usual minimum angle condition. Moreover, the square root of the error in the approximation of the eigenvalue is also bounded by a constant times the estimator. 1999 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v9_n8_p1165_Duran http://hdl.handle.net/20.500.12110/paper_02182025_v9_n8_p1165_Duran
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description In this paper we introduce and analyze an a posteriori error estimator for the approximation of the eigenvalues and eigenvectors of a second-order elliptic problem obtained by the mixed finite element method of Raviart-Thomas of the lowest order. We define an error estimator of the residual type which can be computed locally from the approximate eigenvector and prove that the estimator is equivalent to the norm of the error in the approximation of the eigenvector up to higher order terms. The constants involved in this equivalence depend on the corresponding eigenvalue but are independent of the mesh size, provided the meshes satisfy the usual minimum angle condition. Moreover, the square root of the error in the approximation of the eigenvalue is also bounded by a constant times the estimator.
title A posteriori error estimators for mixed approximations of eigenvalue problems
spellingShingle A posteriori error estimators for mixed approximations of eigenvalue problems
title_short A posteriori error estimators for mixed approximations of eigenvalue problems
title_full A posteriori error estimators for mixed approximations of eigenvalue problems
title_fullStr A posteriori error estimators for mixed approximations of eigenvalue problems
title_full_unstemmed A posteriori error estimators for mixed approximations of eigenvalue problems
title_sort posteriori error estimators for mixed approximations of eigenvalue problems
publishDate 1999
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v9_n8_p1165_Duran
http://hdl.handle.net/20.500.12110/paper_02182025_v9_n8_p1165_Duran
_version_ 1768545002225401856

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