Finite element approximations of the nonhomogeneous fractional Dirichlet problem

Autores
Acosta Rodriguez, Gabriel; Borthagaray Peradotto, Juan Pablo; Heuer, Norbert
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogue of the normal derivative as a Lagrange multiplier in the formulation of the problem. In order to obtain convergence orders for our scheme, regularity estimates are developed both for the solution and for its nonlocal derivative. The method we propose requires that, as meshes are refined, the discrete problems be solved in a family of domains of growing diameter.
Fil: Acosta Rodriguez, Gabriel. 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: Borthagaray Peradotto, Juan Pablo. 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: Heuer, Norbert. Pontificia Universidad Católica de Chile; Chile
Materia
FRACTIONAL LAPLACIAN
FINITE ELEMENTS
A PRIORI ERROR ESTIMATES
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:11336/116922
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/116922
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Finite element approximations of the nonhomogeneous fractional Dirichlet problemAcosta Rodriguez, GabrielBorthagaray Peradotto, Juan PabloHeuer, NorbertFRACTIONAL LAPLACIANFINITE ELEMENTSA PRIORI ERROR ESTIMATEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogue of the normal derivative as a Lagrange multiplier in the formulation of the problem. In order to obtain convergence orders for our scheme, regularity estimates are developed both for the solution and for its nonlocal derivative. The method we propose requires that, as meshes are refined, the discrete problems be solved in a family of domains of growing diameter.Fil: Acosta Rodriguez, Gabriel. 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: Borthagaray Peradotto, Juan Pablo. 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: Heuer, Norbert. Pontificia Universidad Católica de Chile; ChileOxford University Press2018-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/116922Acosta Rodriguez, Gabriel; Borthagaray Peradotto, Juan Pablo; Heuer, Norbert; Finite element approximations of the nonhomogeneous fractional Dirichlet problem; Oxford University Press; Ima Journal Of Numerical Analysis; 39; 3; 5-2018; 1471–15010272-4979CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imajna/advance-article/doi/10.1093/imanum/dry023/4990927info:eu-repo/semantics/altIdentifier/doi/10.1093/imanum/dry023info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:38:45Zoai:ri.conicet.gov.ar:11336/116922instacron: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 10:38:45.359CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Finite element approximations of the nonhomogeneous fractional Dirichlet problem
title Finite element approximations of the nonhomogeneous fractional Dirichlet problem
spellingShingle Finite element approximations of the nonhomogeneous fractional Dirichlet problem
Acosta Rodriguez, Gabriel
FRACTIONAL LAPLACIAN
FINITE ELEMENTS
A PRIORI ERROR ESTIMATES
title_short Finite element approximations of the nonhomogeneous fractional Dirichlet problem
title_full Finite element approximations of the nonhomogeneous fractional Dirichlet problem
title_fullStr Finite element approximations of the nonhomogeneous fractional Dirichlet problem
title_full_unstemmed Finite element approximations of the nonhomogeneous fractional Dirichlet problem
title_sort Finite element approximations of the nonhomogeneous fractional Dirichlet problem
dc.creator.none.fl_str_mv Acosta Rodriguez, Gabriel
Borthagaray Peradotto, Juan Pablo
Heuer, Norbert
author Acosta Rodriguez, Gabriel
author_facet Acosta Rodriguez, Gabriel
Borthagaray Peradotto, Juan Pablo
Heuer, Norbert
author_role author
author2 Borthagaray Peradotto, Juan Pablo
Heuer, Norbert
author2_role author
author
dc.subject.none.fl_str_mv FRACTIONAL LAPLACIAN
FINITE ELEMENTS
A PRIORI ERROR ESTIMATES
topic FRACTIONAL LAPLACIAN
FINITE ELEMENTS
A PRIORI ERROR ESTIMATES
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 study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogue of the normal derivative as a Lagrange multiplier in the formulation of the problem. In order to obtain convergence orders for our scheme, regularity estimates are developed both for the solution and for its nonlocal derivative. The method we propose requires that, as meshes are refined, the discrete problems be solved in a family of domains of growing diameter.
Fil: Acosta Rodriguez, Gabriel. 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: Borthagaray Peradotto, Juan Pablo. 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: Heuer, Norbert. Pontificia Universidad Católica de Chile; Chile
description We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogue of the normal derivative as a Lagrange multiplier in the formulation of the problem. In order to obtain convergence orders for our scheme, regularity estimates are developed both for the solution and for its nonlocal derivative. The method we propose requires that, as meshes are refined, the discrete problems be solved in a family of domains of growing diameter.
publishDate 2018
dc.date.none.fl_str_mv 2018-05
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/11336/116922
Acosta Rodriguez, Gabriel; Borthagaray Peradotto, Juan Pablo; Heuer, Norbert; Finite element approximations of the nonhomogeneous fractional Dirichlet problem; Oxford University Press; Ima Journal Of Numerical Analysis; 39; 3; 5-2018; 1471–1501
0272-4979
CONICET Digital
CONICET
url http://hdl.handle.net/11336/116922
identifier_str_mv Acosta Rodriguez, Gabriel; Borthagaray Peradotto, Juan Pablo; Heuer, Norbert; Finite element approximations of the nonhomogeneous fractional Dirichlet problem; Oxford University Press; Ima Journal Of Numerical Analysis; 39; 3; 5-2018; 1471–1501
0272-4979
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://academic.oup.com/imajna/advance-article/doi/10.1093/imanum/dry023/4990927
info:eu-repo/semantics/altIdentifier/doi/10.1093/imanum/dry023
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 Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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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