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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/55515
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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 Técnicas2025-09-03T09:56:13Zoai: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:34982025-09-03 09:56:13.733CONICET 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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1842269391859744768 |
score |
13.13397 |