Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property

Autores
Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present an adaptive finite element method (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C1 graphs Γ in R{double-struck}d (d ≥ 2). We first derive residual-type a posteriori error estimates that account for the interaction of both the energy error in H1(Γ) and the surface error in W∞1 (Γ) due to approximation of Γ. We devise a marking strategy to reduce the total error estimator, namely a suitably scaled sum of the energy, geometric, and inconsistency error estimators. We prove a conditional contraction property for the sum of the energy error and the total estimator; the conditional statement encodes resolution of Γ in W∞1. We conclude with one numerical experiment that illustrates the theory.
Fil: Mekchay, Khamron. University of Maryland; Estados Unidos
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Nochetto, Ricardo Horacio. University of Maryland; Estados Unidos
Materia
A Posteriori Error Estimate
Adaptive Finite Element Method
Bisection
Contraction
Energy And Geometric Errors
Graphs
Laplace-Beltrami Operator
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:11336/75180
Acceder
id CONICETDig_58f1bfed14cbede71705d4bca053ddb5
oai_identifier_str oai:ri.conicet.gov.ar:11336/75180
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction propertyMekchay, KhamronMorin, PedroNochetto, Ricardo HoracioA Posteriori Error EstimateAdaptive Finite Element MethodBisectionContractionEnergy And Geometric ErrorsGraphsLaplace-Beltrami Operatorhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present an adaptive finite element method (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C1 graphs Γ in R{double-struck}d (d ≥ 2). We first derive residual-type a posteriori error estimates that account for the interaction of both the energy error in H1(Γ) and the surface error in W∞1 (Γ) due to approximation of Γ. We devise a marking strategy to reduce the total error estimator, namely a suitably scaled sum of the energy, geometric, and inconsistency error estimators. We prove a conditional contraction property for the sum of the energy error and the total estimator; the conditional statement encodes resolution of Γ in W∞1. We conclude with one numerical experiment that illustrates the theory.Fil: Mekchay, Khamron. University of Maryland; Estados UnidosFil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Nochetto, Ricardo Horacio. University of Maryland; Estados UnidosAmerican Mathematical Society2011-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/75180Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio; Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property; American Mathematical Society; Mathematics Of Computation; 80; 274; 1-2011; 625-6480025-5718CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2010-02435-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:02:30Zoai:ri.conicet.gov.ar:11336/75180instacron: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:34982025-10-22 12:02:30.545CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
title Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
spellingShingle Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
Mekchay, Khamron
A Posteriori Error Estimate
Adaptive Finite Element Method
Bisection
Contraction
Energy And Geometric Errors
Graphs
Laplace-Beltrami Operator
title_short Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
title_full Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
title_fullStr Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
title_full_unstemmed Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
title_sort Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
dc.creator.none.fl_str_mv Mekchay, Khamron
Morin, Pedro
Nochetto, Ricardo Horacio
author Mekchay, Khamron
author_facet Mekchay, Khamron
Morin, Pedro
Nochetto, Ricardo Horacio
author_role author
author2 Morin, Pedro
Nochetto, Ricardo Horacio
author2_role author
author
dc.subject.none.fl_str_mv A Posteriori Error Estimate
Adaptive Finite Element Method
Bisection
Contraction
Energy And Geometric Errors
Graphs
Laplace-Beltrami Operator
topic A Posteriori Error Estimate
Adaptive Finite Element Method
Bisection
Contraction
Energy And Geometric Errors
Graphs
Laplace-Beltrami Operator
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 present an adaptive finite element method (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C1 graphs Γ in R{double-struck}d (d ≥ 2). We first derive residual-type a posteriori error estimates that account for the interaction of both the energy error in H1(Γ) and the surface error in W∞1 (Γ) due to approximation of Γ. We devise a marking strategy to reduce the total error estimator, namely a suitably scaled sum of the energy, geometric, and inconsistency error estimators. We prove a conditional contraction property for the sum of the energy error and the total estimator; the conditional statement encodes resolution of Γ in W∞1. We conclude with one numerical experiment that illustrates the theory.
Fil: Mekchay, Khamron. University of Maryland; Estados Unidos
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Nochetto, Ricardo Horacio. University of Maryland; Estados Unidos
description We present an adaptive finite element method (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C1 graphs Γ in R{double-struck}d (d ≥ 2). We first derive residual-type a posteriori error estimates that account for the interaction of both the energy error in H1(Γ) and the surface error in W∞1 (Γ) due to approximation of Γ. We devise a marking strategy to reduce the total error estimator, namely a suitably scaled sum of the energy, geometric, and inconsistency error estimators. We prove a conditional contraction property for the sum of the energy error and the total estimator; the conditional statement encodes resolution of Γ in W∞1. We conclude with one numerical experiment that illustrates the theory.
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/11336/75180
Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio; Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property; American Mathematical Society; Mathematics Of Computation; 80; 274; 1-2011; 625-648
0025-5718
CONICET Digital
CONICET
url http://hdl.handle.net/11336/75180
identifier_str_mv Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio; Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property; American Mathematical Society; Mathematics Of Computation; 80; 274; 1-2011; 625-648
0025-5718
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-2010-02435-4
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
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
_version_ 1846782361541279744
score 12.982451

Publicaciones similares