A fractional Laplace equation: Regularity of solutions and finite element approximations

Autores
Acosta Rodriguez, Gabriel; Borthagaray Peradotto, Juan Pablo
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions.
Fil: Acosta Rodriguez, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Borthagaray Peradotto, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Materia
FINITE ELEMENTS
FRACTIONAL LAPLACIAN
GRADED MESHES
WEIGHTED FRACTIONAL NORMS
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:11336/55515
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/55515
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A fractional Laplace equation: Regularity of solutions and finite element approximationsAcosta Rodriguez, GabrielBorthagaray Peradotto, Juan PabloFINITE ELEMENTSFRACTIONAL LAPLACIANGRADED MESHESWEIGHTED FRACTIONAL NORMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions.Fil: Acosta Rodriguez, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Borthagaray Peradotto, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaSociety for Industrial and Applied Mathematics2017-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55515Acosta Rodriguez, Gabriel; Borthagaray Peradotto, Juan Pablo; A fractional Laplace equation: Regularity of solutions and finite element approximations; Society for Industrial and Applied Mathematics; Siam Journal On Numerical Analysis; 55; 2; 1-2017; 472-4950036-1429CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/15M1033952info:eu-repo/semantics/altIdentifier/doi/10.1137/15M1033952info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:00:08Zoai:ri.conicet.gov.ar:11336/55515instacron: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 10:00:08.323CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A fractional Laplace equation: Regularity of solutions and finite element approximations
title A fractional Laplace equation: Regularity of solutions and finite element approximations
spellingShingle A fractional Laplace equation: Regularity of solutions and finite element approximations
Acosta Rodriguez, Gabriel
FINITE ELEMENTS
FRACTIONAL LAPLACIAN
GRADED MESHES
WEIGHTED FRACTIONAL NORMS
title_short A fractional Laplace equation: Regularity of solutions and finite element approximations
title_full A fractional Laplace equation: Regularity of solutions and finite element approximations
title_fullStr A fractional Laplace equation: Regularity of solutions and finite element approximations
title_full_unstemmed A fractional Laplace equation: Regularity of solutions and finite element approximations
title_sort A fractional Laplace equation: Regularity of solutions and finite element approximations
dc.creator.none.fl_str_mv Acosta Rodriguez, Gabriel
Borthagaray Peradotto, Juan Pablo
author Acosta Rodriguez, Gabriel
author_facet Acosta Rodriguez, Gabriel
Borthagaray Peradotto, Juan Pablo
author_role author
author2 Borthagaray Peradotto, Juan Pablo
author2_role author
dc.subject.none.fl_str_mv FINITE ELEMENTS
FRACTIONAL LAPLACIAN
GRADED MESHES
WEIGHTED FRACTIONAL NORMS
topic FINITE ELEMENTS
FRACTIONAL LAPLACIAN
GRADED MESHES
WEIGHTED FRACTIONAL NORMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions.
Fil: Acosta Rodriguez, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Borthagaray Peradotto, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
description This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions.
publishDate 2017
dc.date.none.fl_str_mv 2017-01
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/11336/55515
Acosta Rodriguez, Gabriel; Borthagaray Peradotto, Juan Pablo; A fractional Laplace equation: Regularity of solutions and finite element approximations; Society for Industrial and Applied Mathematics; Siam Journal On Numerical Analysis; 55; 2; 1-2017; 472-495
0036-1429
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55515
identifier_str_mv Acosta Rodriguez, Gabriel; Borthagaray Peradotto, Juan Pablo; A fractional Laplace equation: Regularity of solutions and finite element approximations; Society for Industrial and Applied Mathematics; Siam Journal On Numerical Analysis; 55; 2; 1-2017; 472-495
0036-1429
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://epubs.siam.org/doi/abs/10.1137/15M1033952
info:eu-repo/semantics/altIdentifier/doi/10.1137/15M1033952
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 Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
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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