A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes

The existence and uniqueness of the discrete solutions of a porous medium equation with diffusion are demonstrated. The Cauchy problem contains a fractional Laplacian and it is equivalent to the extension formulation in the sense of trace and harmonic extension operators. By using the generalized fi...

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Detalles Bibliográficos
Autores: García, Ángel, Negreanu Pruna, Mihaela, Ureña, Francisco, Vargas, Antonio M.
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/7344
Acceso en línea:https://hdl.handle.net/20.500.14352/7344
Access Level:acceso abierto
Palabra clave:517
Fractional Laplacian
Generalized finite difference method
Discrete maximum principle
Convergence
Análisis matemático
1202 Análisis y Análisis Funcional
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spelling A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular MeshesGarcía, ÁngelNegreanu Pruna, MihaelaUreña, FranciscoVargas, Antonio M.517Fractional LaplacianGeneralized finite difference methodDiscrete maximum principleConvergenceAnálisis matemático1202 Análisis y Análisis FuncionalThe existence and uniqueness of the discrete solutions of a porous medium equation with diffusion are demonstrated. The Cauchy problem contains a fractional Laplacian and it is equivalent to the extension formulation in the sense of trace and harmonic extension operators. By using the generalized finite difference method, we obtain the convergence of the numerical solution to the classical/theoretical solution of the equation for nonnegative initial data sufficiently smooth and bounded. This procedure allows us to use meshes with complicated geometry (more realistic) or with an irregular distribution of nodes (providing more accurate solutions where needed). Some numerical results are presented in arbitrary irregular meshes to illustrate the potential of the method.Universidad Complutense de Madrid20212021-01-0120212021-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/7344reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/73442026-06-02T12:44:21Z
dc.title.none.fl_str_mv A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
spellingShingle A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
García, Ángel
517
Fractional Laplacian
Generalized finite difference method
Discrete maximum principle
Convergence
Análisis matemático
1202 Análisis y Análisis Funcional
title_short A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_full A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_fullStr A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_full_unstemmed A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
title_sort A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes
dc.creator.none.fl_str_mv García, Ángel
Negreanu Pruna, Mihaela
Ureña, Francisco
Vargas, Antonio M.
author García, Ángel
author_facet García, Ángel
Negreanu Pruna, Mihaela
Ureña, Francisco
Vargas, Antonio M.
author_role author
author2 Negreanu Pruna, Mihaela
Ureña, Francisco
Vargas, Antonio M.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517
Fractional Laplacian
Generalized finite difference method
Discrete maximum principle
Convergence
Análisis matemático
1202 Análisis y Análisis Funcional
topic 517
Fractional Laplacian
Generalized finite difference method
Discrete maximum principle
Convergence
Análisis matemático
1202 Análisis y Análisis Funcional
description The existence and uniqueness of the discrete solutions of a porous medium equation with diffusion are demonstrated. The Cauchy problem contains a fractional Laplacian and it is equivalent to the extension formulation in the sense of trace and harmonic extension operators. By using the generalized finite difference method, we obtain the convergence of the numerical solution to the classical/theoretical solution of the equation for nonnegative initial data sufficiently smooth and bounded. This procedure allows us to use meshes with complicated geometry (more realistic) or with an irregular distribution of nodes (providing more accurate solutions where needed). Some numerical results are presented in arbitrary irregular meshes to illustrate the potential of the method.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01
2021
2021-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/7344
url https://hdl.handle.net/20.500.14352/7344
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución 3.0 España
https://creativecommons.org/licenses/by/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución 3.0 España
https://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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