Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra

Autores
Acosta, Gerardo Gabriel; Apel, Thomas; Duran, Ricardo Guillermo; Lombardi, Ariel Luis
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three-dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject, and the results obtained are more general in several aspects. First, intermediate regularity is allowed; that is, for the Raviart-Thomas interpolation of degree k ≥ 0, we prove error estimates of order j + 1 when the vector field being approximated has components in WJ+1,p, for triangles or tetrahedra, where 0 ≤ j ≤ k and 1 ≤ p ≤ ∞. These results are new even in the two-dimensional case. Indeed, the estimate was known only in the case j = k. On the other hand, in the three-dimensional case, results under the maximum angle condition were known only for k = 0.
Fil: Acosta, Gerardo Gabriel. 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: Apel, Thomas. Institut fur Mathematik und Bauinformatik, Universit at der Bundeswehr Munchen; Armenia
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: Lombardi, Ariel Luis. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
ANISOTROPIC FINITE ELEMENTS
MIXED FINITE ELEMENTS
RAVIART-THOMAS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/127529
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedraAcosta, Gerardo GabrielApel, ThomasDuran, Ricardo GuillermoLombardi, Ariel LuisANISOTROPIC FINITE ELEMENTSMIXED FINITE ELEMENTSRAVIART-THOMAShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three-dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject, and the results obtained are more general in several aspects. First, intermediate regularity is allowed; that is, for the Raviart-Thomas interpolation of degree k ≥ 0, we prove error estimates of order j + 1 when the vector field being approximated has components in WJ+1,p, for triangles or tetrahedra, where 0 ≤ j ≤ k and 1 ≤ p ≤ ∞. These results are new even in the two-dimensional case. Indeed, the estimate was known only in the case j = k. On the other hand, in the three-dimensional case, results under the maximum angle condition were known only for k = 0.Fil: Acosta, Gerardo Gabriel. 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: Apel, Thomas. Institut fur Mathematik und Bauinformatik, Universit at der Bundeswehr Munchen; ArmeniaFil: 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: Lombardi, Ariel Luis. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Mathematical Society2011-01info: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/11336/127529Acosta, Gerardo Gabriel; Apel, Thomas; Duran, Ricardo Guillermo; Lombardi, Ariel Luis; Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra; American Mathematical Society; Mathematics of Computation; 80; 273; 1-2011; 141-1631088-6842CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0809.2072info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02406-8/info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2010-02406-8info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:22:26Zoai:ri.conicet.gov.ar:11336/127529instacron: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:34982025-09-29 10:22:26.992CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
title Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
spellingShingle Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
Acosta, Gerardo Gabriel
ANISOTROPIC FINITE ELEMENTS
MIXED FINITE ELEMENTS
RAVIART-THOMAS
title_short Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
title_full Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
title_fullStr Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
title_full_unstemmed Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
title_sort Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
dc.creator.none.fl_str_mv Acosta, Gerardo Gabriel
Apel, Thomas
Duran, Ricardo Guillermo
Lombardi, Ariel Luis
author Acosta, Gerardo Gabriel
author_facet Acosta, Gerardo Gabriel
Apel, Thomas
Duran, Ricardo Guillermo
Lombardi, Ariel Luis
author_role author
author2 Apel, Thomas
Duran, Ricardo Guillermo
Lombardi, Ariel Luis
author2_role author
author
author
dc.subject.none.fl_str_mv ANISOTROPIC FINITE ELEMENTS
MIXED FINITE ELEMENTS
RAVIART-THOMAS
topic ANISOTROPIC FINITE ELEMENTS
MIXED FINITE ELEMENTS
RAVIART-THOMAS
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 prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three-dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject, and the results obtained are more general in several aspects. First, intermediate regularity is allowed; that is, for the Raviart-Thomas interpolation of degree k ≥ 0, we prove error estimates of order j + 1 when the vector field being approximated has components in WJ+1,p, for triangles or tetrahedra, where 0 ≤ j ≤ k and 1 ≤ p ≤ ∞. These results are new even in the two-dimensional case. Indeed, the estimate was known only in the case j = k. On the other hand, in the three-dimensional case, results under the maximum angle condition were known only for k = 0.
Fil: Acosta, Gerardo Gabriel. 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: Apel, Thomas. Institut fur Mathematik und Bauinformatik, Universit at der Bundeswehr Munchen; Armenia
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: Lombardi, Ariel Luis. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three-dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject, and the results obtained are more general in several aspects. First, intermediate regularity is allowed; that is, for the Raviart-Thomas interpolation of degree k ≥ 0, we prove error estimates of order j + 1 when the vector field being approximated has components in WJ+1,p, for triangles or tetrahedra, where 0 ≤ j ≤ k and 1 ≤ p ≤ ∞. These results are new even in the two-dimensional case. Indeed, the estimate was known only in the case j = k. On the other hand, in the three-dimensional case, results under the maximum angle condition were known only for k = 0.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
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/11336/127529
Acosta, Gerardo Gabriel; Apel, Thomas; Duran, Ricardo Guillermo; Lombardi, Ariel Luis; Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra; American Mathematical Society; Mathematics of Computation; 80; 273; 1-2011; 141-163
1088-6842
CONICET Digital
CONICET
url http://hdl.handle.net/11336/127529
identifier_str_mv Acosta, Gerardo Gabriel; Apel, Thomas; Duran, Ricardo Guillermo; Lombardi, Ariel Luis; Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra; American Mathematical Society; Mathematics of Computation; 80; 273; 1-2011; 141-163
1088-6842
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0809.2072
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02406-8/
info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2010-02406-8
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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 13.070432

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