High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates

Autores
Bonito, Andrea; Cascón, José Manuel; Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a new AFEM for the Laplace–Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W∞1 and piecewise in a suitable Besov class embedded in C1 , α with α∈ (0 , 1 ]. The idea is to have the surface sufficiently well resolved in W∞1 relative to the current resolution of the PDE in H1. This gives rise to a conditional contraction property of the PDE module. We present a suitable approximation class and discuss its relation to Besov regularity of the surface, solution, and forcing. We prove optimal convergence rates for AFEM which are dictated by the worst decay rate of the surface error in W∞1 and PDE error in H1.
Fil: Bonito, Andrea. Texas A&M University; Estados Unidos
Fil: Cascón, José Manuel. Universidad de Salamanca; España
Fil: Mekchay, Khamron. Chulalongkorn University; Tailandia
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral; Argentina
Fil: Nochetto, Ricardo Horacio. University of Maryland; Estados Unidos
Materia
A POSTERIORI ERROR ESTIMATES
ADAPTIVE FINITE ELEMENT METHOD
CONVERGENCE RATES
HIGHER ORDER
LAPLACE–BELTRAMI OPERATOR
PARAMETRIC SURFACES
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:11336/70885
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/70885
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling High-Order AFEM for the Laplace–Beltrami Operator: Convergence RatesBonito, AndreaCascón, José ManuelMekchay, KhamronMorin, PedroNochetto, Ricardo HoracioA POSTERIORI ERROR ESTIMATESADAPTIVE FINITE ELEMENT METHODCONVERGENCE RATESHIGHER ORDERLAPLACE–BELTRAMI OPERATORPARAMETRIC SURFACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a new AFEM for the Laplace–Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W∞1 and piecewise in a suitable Besov class embedded in C1 , α with α∈ (0 , 1 ]. The idea is to have the surface sufficiently well resolved in W∞1 relative to the current resolution of the PDE in H1. This gives rise to a conditional contraction property of the PDE module. We present a suitable approximation class and discuss its relation to Besov regularity of the surface, solution, and forcing. We prove optimal convergence rates for AFEM which are dictated by the worst decay rate of the surface error in W∞1 and PDE error in H1.Fil: Bonito, Andrea. Texas A&M University; Estados UnidosFil: Cascón, José Manuel. Universidad de Salamanca; EspañaFil: Mekchay, Khamron. Chulalongkorn University; TailandiaFil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral; ArgentinaFil: Nochetto, Ricardo Horacio. University of Maryland; Estados UnidosSpringer2016-12info: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/11336/70885Bonito, Andrea; Cascón, José Manuel; Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio; High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates; Springer; Foundations Of Computational Mathematics; 16; 6; 12-2016; 1473-15391615-33751615-3383CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s10208-016-9335-7info:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-016-9335-7info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1511.05019info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:51:41Zoai:ri.conicet.gov.ar:11336/70885instacron: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 11:51:42.236CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
title High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
spellingShingle High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
Bonito, Andrea
A POSTERIORI ERROR ESTIMATES
ADAPTIVE FINITE ELEMENT METHOD
CONVERGENCE RATES
HIGHER ORDER
LAPLACE–BELTRAMI OPERATOR
PARAMETRIC SURFACES
title_short High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
title_full High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
title_fullStr High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
title_full_unstemmed High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
title_sort High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
dc.creator.none.fl_str_mv Bonito, Andrea
Cascón, José Manuel
Mekchay, Khamron
Morin, Pedro
Nochetto, Ricardo Horacio
author Bonito, Andrea
author_facet Bonito, Andrea
Cascón, José Manuel
Mekchay, Khamron
Morin, Pedro
Nochetto, Ricardo Horacio
author_role author
author2 Cascón, José Manuel
Mekchay, Khamron
Morin, Pedro
Nochetto, Ricardo Horacio
author2_role author
author
author
author
dc.subject.none.fl_str_mv A POSTERIORI ERROR ESTIMATES
ADAPTIVE FINITE ELEMENT METHOD
CONVERGENCE RATES
HIGHER ORDER
LAPLACE–BELTRAMI OPERATOR
PARAMETRIC SURFACES
topic A POSTERIORI ERROR ESTIMATES
ADAPTIVE FINITE ELEMENT METHOD
CONVERGENCE RATES
HIGHER ORDER
LAPLACE–BELTRAMI OPERATOR
PARAMETRIC SURFACES
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 a new AFEM for the Laplace–Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W∞1 and piecewise in a suitable Besov class embedded in C1 , α with α∈ (0 , 1 ]. The idea is to have the surface sufficiently well resolved in W∞1 relative to the current resolution of the PDE in H1. This gives rise to a conditional contraction property of the PDE module. We present a suitable approximation class and discuss its relation to Besov regularity of the surface, solution, and forcing. We prove optimal convergence rates for AFEM which are dictated by the worst decay rate of the surface error in W∞1 and PDE error in H1.
Fil: Bonito, Andrea. Texas A&M University; Estados Unidos
Fil: Cascón, José Manuel. Universidad de Salamanca; España
Fil: Mekchay, Khamron. Chulalongkorn University; Tailandia
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral; Argentina
Fil: Nochetto, Ricardo Horacio. University of Maryland; Estados Unidos
description We present a new AFEM for the Laplace–Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W∞1 and piecewise in a suitable Besov class embedded in C1 , α with α∈ (0 , 1 ]. The idea is to have the surface sufficiently well resolved in W∞1 relative to the current resolution of the PDE in H1. This gives rise to a conditional contraction property of the PDE module. We present a suitable approximation class and discuss its relation to Besov regularity of the surface, solution, and forcing. We prove optimal convergence rates for AFEM which are dictated by the worst decay rate of the surface error in W∞1 and PDE error in H1.
publishDate 2016
dc.date.none.fl_str_mv 2016-12
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/11336/70885
Bonito, Andrea; Cascón, José Manuel; Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio; High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates; Springer; Foundations Of Computational Mathematics; 16; 6; 12-2016; 1473-1539
1615-3375
1615-3383
CONICET Digital
CONICET
url http://hdl.handle.net/11336/70885
identifier_str_mv Bonito, Andrea; Cascón, José Manuel; Mekchay, Khamron; Morin, Pedro; Nochetto, Ricardo Horacio; High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates; Springer; Foundations Of Computational Mathematics; 16; 6; 12-2016; 1473-1539
1615-3375
1615-3383
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s10208-016-9335-7
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-016-9335-7
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1511.05019
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
_version_ 1846782204641804288
score 12.982451

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