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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/217068
Ver los metadatos del registro completo
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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 Técnicas2025-09-03T09:45:17Zoai: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:34982025-09-03 09:45:17.301CONICET 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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1842268719749791744 |
score |
13.13397 |