Numerical approximations for a fully fractional Allen-Cahn equation

Autores
Acosta Rodriguez, Gabriel; Mastroberti Bersetche, Francisco Vicente
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace the standard local operators. Piecewise linear finite elements and convolution quadratures are the basic tools involved in the presented numerical method. Error analysis and implementation issues are addressed together with the needed results of regularity for the continuous model. Also, the asymptotic behavior of solutions, for a vanishing fractional parameter and usual derivative in time, is discussed within the framework of the Γ-convergence theory.
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: Mastroberti Bersetche, Francisco Vicente. 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
Materia
CAPUTO DERIVATIVE
FRACTIONAL LAPLACIAN
SEMILINEAR EVOLUTION PROBLEMS
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:11336/217068
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/217068
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Numerical approximations for a fully fractional Allen-Cahn equationAcosta Rodriguez, GabrielMastroberti Bersetche, Francisco VicenteCAPUTO DERIVATIVEFRACTIONAL LAPLACIANSEMILINEAR EVOLUTION PROBLEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace the standard local operators. Piecewise linear finite elements and convolution quadratures are the basic tools involved in the presented numerical method. Error analysis and implementation issues are addressed together with the needed results of regularity for the continuous model. Also, the asymptotic behavior of solutions, for a vanishing fractional parameter and usual derivative in time, is discussed within the framework of the Γ-convergence theory.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: Mastroberti Bersetche, Francisco Vicente. 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"; ArgentinaEDP Sciences2020-04info: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/11336/217068Acosta Rodriguez, Gabriel; Mastroberti Bersetche, Francisco Vicente; Numerical approximations for a fully fractional Allen-Cahn equation; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 55; 4-2020; 1-260764-583X2804-7214CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.esaim-m2an.org/10.1051/m2an/2020022info:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2020022info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:35:41Zoai:ri.conicet.gov.ar:11336/217068instacron: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 09:35:41.453CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Numerical approximations for a fully fractional Allen-Cahn equation
title Numerical approximations for a fully fractional Allen-Cahn equation
spellingShingle Numerical approximations for a fully fractional Allen-Cahn equation
Acosta Rodriguez, Gabriel
CAPUTO DERIVATIVE
FRACTIONAL LAPLACIAN
SEMILINEAR EVOLUTION PROBLEMS
title_short Numerical approximations for a fully fractional Allen-Cahn equation
title_full Numerical approximations for a fully fractional Allen-Cahn equation
title_fullStr Numerical approximations for a fully fractional Allen-Cahn equation
title_full_unstemmed Numerical approximations for a fully fractional Allen-Cahn equation
title_sort Numerical approximations for a fully fractional Allen-Cahn equation
dc.creator.none.fl_str_mv Acosta Rodriguez, Gabriel
Mastroberti Bersetche, Francisco Vicente
author Acosta Rodriguez, Gabriel
author_facet Acosta Rodriguez, Gabriel
Mastroberti Bersetche, Francisco Vicente
author_role author
author2 Mastroberti Bersetche, Francisco Vicente
author2_role author
dc.subject.none.fl_str_mv CAPUTO DERIVATIVE
FRACTIONAL LAPLACIAN
SEMILINEAR EVOLUTION PROBLEMS
topic CAPUTO DERIVATIVE
FRACTIONAL LAPLACIAN
SEMILINEAR EVOLUTION PROBLEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace the standard local operators. Piecewise linear finite elements and convolution quadratures are the basic tools involved in the presented numerical method. Error analysis and implementation issues are addressed together with the needed results of regularity for the continuous model. Also, the asymptotic behavior of solutions, for a vanishing fractional parameter and usual derivative in time, is discussed within the framework of the Γ-convergence theory.
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: Mastroberti Bersetche, Francisco Vicente. 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
description A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace the standard local operators. Piecewise linear finite elements and convolution quadratures are the basic tools involved in the presented numerical method. Error analysis and implementation issues are addressed together with the needed results of regularity for the continuous model. Also, the asymptotic behavior of solutions, for a vanishing fractional parameter and usual derivative in time, is discussed within the framework of the Γ-convergence theory.
publishDate 2020
dc.date.none.fl_str_mv 2020-04
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/11336/217068
Acosta Rodriguez, Gabriel; Mastroberti Bersetche, Francisco Vicente; Numerical approximations for a fully fractional Allen-Cahn equation; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 55; 4-2020; 1-26
0764-583X
2804-7214
CONICET Digital
CONICET
url http://hdl.handle.net/11336/217068
identifier_str_mv Acosta Rodriguez, Gabriel; Mastroberti Bersetche, Francisco Vicente; Numerical approximations for a fully fractional Allen-Cahn equation; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 55; 4-2020; 1-26
0764-583X
2804-7214
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.esaim-m2an.org/10.1051/m2an/2020022
info:eu-repo/semantics/altIdentifier/doi/10.1051/m2an/2020022
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 EDP Sciences
publisher.none.fl_str_mv EDP Sciences
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 13.069144

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