A posteriori error estimates for non-conforming approximation of eigenvalue problems

Autores
Dari, Enzo Alberto; Duran, Ricardo Guillermo; Padra, Claudio
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix– Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the error estimator is equivalent to the energy norm of the eigenvector error up to higher order terms. Moreover, we prove that our estimator provides an upper bound for the error in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on our error estimator in two and three dimensions. These examples show that the error in the adaptive procedure is optimal in terms of the number of degrees of freedom.
Fil: Dari, Enzo Alberto. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Padra, Claudio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
A POSTERIORI ERROR ESTIMATES
NON CONFORMING METHODS
EIGENVALUES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19935
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19935
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A posteriori error estimates for non-conforming approximation of eigenvalue problemsDari, Enzo AlbertoDuran, Ricardo GuillermoPadra, ClaudioA POSTERIORI ERROR ESTIMATESNON CONFORMING METHODSEIGENVALUEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix– Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the error estimator is equivalent to the energy norm of the eigenvector error up to higher order terms. Moreover, we prove that our estimator provides an upper bound for the error in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on our error estimator in two and three dimensions. These examples show that the error in the adaptive procedure is optimal in terms of the number of degrees of freedom.Fil: Dari, Enzo Alberto. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Padra, Claudio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2012-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19935Dari, Enzo Alberto; Duran, Ricardo Guillermo; Padra, Claudio; A posteriori error estimates for non-conforming approximation of eigenvalue problems; Elsevier Science; Applied Numerical Mathematics; 62; 5; 5-2012; 580-5910168-9274CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.apnum.2012.01.005info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0168927412000220info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T10:47:10Zoai:ri.conicet.gov.ar:11336/19935instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-17 10:47:11.196CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A posteriori error estimates for non-conforming approximation of eigenvalue problems
title A posteriori error estimates for non-conforming approximation of eigenvalue problems
spellingShingle A posteriori error estimates for non-conforming approximation of eigenvalue problems
Dari, Enzo Alberto
A POSTERIORI ERROR ESTIMATES
NON CONFORMING METHODS
EIGENVALUES
title_short A posteriori error estimates for non-conforming approximation of eigenvalue problems
title_full A posteriori error estimates for non-conforming approximation of eigenvalue problems
title_fullStr A posteriori error estimates for non-conforming approximation of eigenvalue problems
title_full_unstemmed A posteriori error estimates for non-conforming approximation of eigenvalue problems
title_sort A posteriori error estimates for non-conforming approximation of eigenvalue problems
dc.creator.none.fl_str_mv Dari, Enzo Alberto
Duran, Ricardo Guillermo
Padra, Claudio
author Dari, Enzo Alberto
author_facet Dari, Enzo Alberto
Duran, Ricardo Guillermo
Padra, Claudio
author_role author
author2 Duran, Ricardo Guillermo
Padra, Claudio
author2_role author
author
dc.subject.none.fl_str_mv A POSTERIORI ERROR ESTIMATES
NON CONFORMING METHODS
EIGENVALUES
topic A POSTERIORI ERROR ESTIMATES
NON CONFORMING METHODS
EIGENVALUES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix– Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the error estimator is equivalent to the energy norm of the eigenvector error up to higher order terms. Moreover, we prove that our estimator provides an upper bound for the error in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on our error estimator in two and three dimensions. These examples show that the error in the adaptive procedure is optimal in terms of the number of degrees of freedom.
Fil: Dari, Enzo Alberto. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Padra, Claudio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix– Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the error estimator is equivalent to the energy norm of the eigenvector error up to higher order terms. Moreover, we prove that our estimator provides an upper bound for the error in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on our error estimator in two and three dimensions. These examples show that the error in the adaptive procedure is optimal in terms of the number of degrees of freedom.
publishDate 2012
dc.date.none.fl_str_mv 2012-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/19935
Dari, Enzo Alberto; Duran, Ricardo Guillermo; Padra, Claudio; A posteriori error estimates for non-conforming approximation of eigenvalue problems; Elsevier Science; Applied Numerical Mathematics; 62; 5; 5-2012; 580-591
0168-9274
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19935
identifier_str_mv Dari, Enzo Alberto; Duran, Ricardo Guillermo; Padra, Claudio; A posteriori error estimates for non-conforming approximation of eigenvalue problems; Elsevier Science; Applied Numerical Mathematics; 62; 5; 5-2012; 580-591
0168-9274
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.apnum.2012.01.005
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0168927412000220
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.001348

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