A Posteriori Error Estimators for Hierarchical B-Spline Discretizations

Autores
Buffa, Annalisa; Garau, Eduardo Mario
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We obtain a global upper bound for the energy error over arbitrary hierarchical mesh configurations which simplifies the implementation of adaptive refinement strategies. The theory hinges on some weighted Poincaré type inequalities where the B-spline basis functions are the weights appearing in the norms. Such inequalities are derived following the lines in (Veeser and Verfürth, 2009), where the case of standard finite elements is considered. Additionally, we present numerical experiments that show the efficiency of the error estimators independently of the degree of the splines used for the discretization, together with an adaptive algorithm guided by these local estimators that yields optimal meshes and rates of convergence, exhibiting an excellent performance.
Fil: Buffa, Annalisa. École Polytechnique Fédérale de Lausanne; Suiza. Consiglio Nazionale Delle Ricerche. Instituto Dimatemática Applicata E Tecnologie Informatiche; Italia
Fil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral; Argentina
Materia
A posteriori error estimators
Adaptivity
Hierarchical splines
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:11336/89154
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/89154
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A Posteriori Error Estimators for Hierarchical B-Spline DiscretizationsBuffa, AnnalisaGarau, Eduardo MarioA posteriori error estimatorsAdaptivityHierarchical splineshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We obtain a global upper bound for the energy error over arbitrary hierarchical mesh configurations which simplifies the implementation of adaptive refinement strategies. The theory hinges on some weighted Poincaré type inequalities where the B-spline basis functions are the weights appearing in the norms. Such inequalities are derived following the lines in (Veeser and Verfürth, 2009), where the case of standard finite elements is considered. Additionally, we present numerical experiments that show the efficiency of the error estimators independently of the degree of the splines used for the discretization, together with an adaptive algorithm guided by these local estimators that yields optimal meshes and rates of convergence, exhibiting an excellent performance.Fil: Buffa, Annalisa. École Polytechnique Fédérale de Lausanne; Suiza. Consiglio Nazionale Delle Ricerche. Instituto Dimatemática Applicata E Tecnologie Informatiche; ItaliaFil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral; ArgentinaWorld Scientific2018-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/89154Buffa, Annalisa; Garau, Eduardo Mario; A Posteriori Error Estimators for Hierarchical B-Spline Discretizations; World Scientific; Mathematical Models And Methods In Applied Sciences; 28; 8; 7-2018; 1453-14800218-20251793-6314CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/worldscinet/m3asinfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202518500392info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:12:51Zoai:ri.conicet.gov.ar:11336/89154instacron: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 11:12:51.612CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Posteriori Error Estimators for Hierarchical B-Spline Discretizations
title A Posteriori Error Estimators for Hierarchical B-Spline Discretizations
spellingShingle A Posteriori Error Estimators for Hierarchical B-Spline Discretizations
Buffa, Annalisa
A posteriori error estimators
Adaptivity
Hierarchical splines
title_short A Posteriori Error Estimators for Hierarchical B-Spline Discretizations
title_full A Posteriori Error Estimators for Hierarchical B-Spline Discretizations
title_fullStr A Posteriori Error Estimators for Hierarchical B-Spline Discretizations
title_full_unstemmed A Posteriori Error Estimators for Hierarchical B-Spline Discretizations
title_sort A Posteriori Error Estimators for Hierarchical B-Spline Discretizations
dc.creator.none.fl_str_mv Buffa, Annalisa
Garau, Eduardo Mario
author Buffa, Annalisa
author_facet Buffa, Annalisa
Garau, Eduardo Mario
author_role author
author2 Garau, Eduardo Mario
author2_role author
dc.subject.none.fl_str_mv A posteriori error estimators
Adaptivity
Hierarchical splines
topic A posteriori error estimators
Adaptivity
Hierarchical splines
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We obtain a global upper bound for the energy error over arbitrary hierarchical mesh configurations which simplifies the implementation of adaptive refinement strategies. The theory hinges on some weighted Poincaré type inequalities where the B-spline basis functions are the weights appearing in the norms. Such inequalities are derived following the lines in (Veeser and Verfürth, 2009), where the case of standard finite elements is considered. Additionally, we present numerical experiments that show the efficiency of the error estimators independently of the degree of the splines used for the discretization, together with an adaptive algorithm guided by these local estimators that yields optimal meshes and rates of convergence, exhibiting an excellent performance.
Fil: Buffa, Annalisa. École Polytechnique Fédérale de Lausanne; Suiza. Consiglio Nazionale Delle Ricerche. Instituto Dimatemática Applicata E Tecnologie Informatiche; Italia
Fil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral; Argentina
description In this paper we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We obtain a global upper bound for the energy error over arbitrary hierarchical mesh configurations which simplifies the implementation of adaptive refinement strategies. The theory hinges on some weighted Poincaré type inequalities where the B-spline basis functions are the weights appearing in the norms. Such inequalities are derived following the lines in (Veeser and Verfürth, 2009), where the case of standard finite elements is considered. Additionally, we present numerical experiments that show the efficiency of the error estimators independently of the degree of the splines used for the discretization, together with an adaptive algorithm guided by these local estimators that yields optimal meshes and rates of convergence, exhibiting an excellent performance.
publishDate 2018
dc.date.none.fl_str_mv 2018-07
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/11336/89154
Buffa, Annalisa; Garau, Eduardo Mario; A Posteriori Error Estimators for Hierarchical B-Spline Discretizations; World Scientific; Mathematical Models And Methods In Applied Sciences; 28; 8; 7-2018; 1453-1480
0218-2025
1793-6314
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89154
identifier_str_mv Buffa, Annalisa; Garau, Eduardo Mario; A Posteriori Error Estimators for Hierarchical B-Spline Discretizations; World Scientific; Mathematical Models And Methods In Applied Sciences; 28; 8; 7-2018; 1453-1480
0218-2025
1793-6314
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://www.worldscientific.com/worldscinet/m3as
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202518500392
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 World Scientific
publisher.none.fl_str_mv World Scientific
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 12.982451

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