An hp finite element adaptive scheme to solve the Poisson problem on curved domains

Autores
Armentano, Maria Gabriela; Padra, Claudio; Scheble, Mario
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work, we introduce an hp finite element method for two-dimensional Poisson problems on curved domains using curved elements. We obtain a priori error estimates and define a local a posteriori error estimator of residual type. We show, under appropriate assumptions about the curved domain, the global reliability and the local efficiency of the estimator. More precisely, we prove that the estimator is equivalent to the energy norm of the error up to higher-order terms. The equivalence constant of the efficiency estimate depends on the polynomial degree. We also present an hp adaptive algorithm and several numerical tests which show the performance of the adaptive strategy.
Fil: Armentano, Maria Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Scheble, Mario. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Materia
A POSTERIORI ERROR ESTIMATES
CURVED DOMAINS
FINITE ELEMENTS
HP VERSION
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:11336/120188
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/120188
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling An hp finite element adaptive scheme to solve the Poisson problem on curved domainsArmentano, Maria GabrielaPadra, ClaudioScheble, MarioA POSTERIORI ERROR ESTIMATESCURVED DOMAINSFINITE ELEMENTSHP VERSIONhttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work, we introduce an hp finite element method for two-dimensional Poisson problems on curved domains using curved elements. We obtain a priori error estimates and define a local a posteriori error estimator of residual type. We show, under appropriate assumptions about the curved domain, the global reliability and the local efficiency of the estimator. More precisely, we prove that the estimator is equivalent to the energy norm of the error up to higher-order terms. The equivalence constant of the efficiency estimate depends on the polynomial degree. We also present an hp adaptive algorithm and several numerical tests which show the performance of the adaptive strategy.Fil: Armentano, Maria Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Scheble, Mario. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaSpringer2015-07info: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/11336/120188Armentano, Maria Gabriela; Padra, Claudio; Scheble, Mario; An hp finite element adaptive scheme to solve the Poisson problem on curved domains; Springer; Computational And Applied Mathematics; 34; 2; 7-2015; 705-7270377-0427CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-014-0133-zinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s40314-014-0133-zinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:13:41Zoai:ri.conicet.gov.ar:11336/120188instacron: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:34982025-09-10 13:13:41.951CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An hp finite element adaptive scheme to solve the Poisson problem on curved domains
title An hp finite element adaptive scheme to solve the Poisson problem on curved domains
spellingShingle An hp finite element adaptive scheme to solve the Poisson problem on curved domains
Armentano, Maria Gabriela
A POSTERIORI ERROR ESTIMATES
CURVED DOMAINS
FINITE ELEMENTS
HP VERSION
title_short An hp finite element adaptive scheme to solve the Poisson problem on curved domains
title_full An hp finite element adaptive scheme to solve the Poisson problem on curved domains
title_fullStr An hp finite element adaptive scheme to solve the Poisson problem on curved domains
title_full_unstemmed An hp finite element adaptive scheme to solve the Poisson problem on curved domains
title_sort An hp finite element adaptive scheme to solve the Poisson problem on curved domains
dc.creator.none.fl_str_mv Armentano, Maria Gabriela
Padra, Claudio
Scheble, Mario
author Armentano, Maria Gabriela
author_facet Armentano, Maria Gabriela
Padra, Claudio
Scheble, Mario
author_role author
author2 Padra, Claudio
Scheble, Mario
author2_role author
author
dc.subject.none.fl_str_mv A POSTERIORI ERROR ESTIMATES
CURVED DOMAINS
FINITE ELEMENTS
HP VERSION
topic A POSTERIORI ERROR ESTIMATES
CURVED DOMAINS
FINITE ELEMENTS
HP VERSION
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work, we introduce an hp finite element method for two-dimensional Poisson problems on curved domains using curved elements. We obtain a priori error estimates and define a local a posteriori error estimator of residual type. We show, under appropriate assumptions about the curved domain, the global reliability and the local efficiency of the estimator. More precisely, we prove that the estimator is equivalent to the energy norm of the error up to higher-order terms. The equivalence constant of the efficiency estimate depends on the polynomial degree. We also present an hp adaptive algorithm and several numerical tests which show the performance of the adaptive strategy.
Fil: Armentano, Maria Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Scheble, Mario. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
description In this work, we introduce an hp finite element method for two-dimensional Poisson problems on curved domains using curved elements. We obtain a priori error estimates and define a local a posteriori error estimator of residual type. We show, under appropriate assumptions about the curved domain, the global reliability and the local efficiency of the estimator. More precisely, we prove that the estimator is equivalent to the energy norm of the error up to higher-order terms. The equivalence constant of the efficiency estimate depends on the polynomial degree. We also present an hp adaptive algorithm and several numerical tests which show the performance of the adaptive strategy.
publishDate 2015
dc.date.none.fl_str_mv 2015-07
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/11336/120188
Armentano, Maria Gabriela; Padra, Claudio; Scheble, Mario; An hp finite element adaptive scheme to solve the Poisson problem on curved domains; Springer; Computational And Applied Mathematics; 34; 2; 7-2015; 705-727
0377-0427
CONICET Digital
CONICET
url http://hdl.handle.net/11336/120188
identifier_str_mv Armentano, Maria Gabriela; Padra, Claudio; Scheble, Mario; An hp finite element adaptive scheme to solve the Poisson problem on curved domains; Springer; Computational And Applied Mathematics; 34; 2; 7-2015; 705-727
0377-0427
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-014-0133-z
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s40314-014-0133-z
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 Springer
publisher.none.fl_str_mv Springer
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 12.993085

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