A Finite Difference Method for the Variational p-Laplacian

We propose a new monotone finite difference discretization for the variational p-Laplace operator, pu = div(|∇u|p−2∇u), and present a convergent numerical scheme for related Dirichlet problems. The resulting nonlinear system is solved using two different methods: one based on Newton-Raphson and one...

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Detalhes bibliográficos
Autores: Del Teso Méndez, Félix, Lindgren, Erik
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71302
Acesso em linha:https://hdl.handle.net/20.500.14352/71302
Access Level:acceso abierto
Palavra-chave:p-Laplacian
Finite difference
Mean value property
Nonhomogeneous Dirichlet problem
Viscosity solutions
Dynamic programming principle
Análisis matemático
1202 Análisis y Análisis Funcional
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spelling A Finite Difference Method for the Variational p-LaplacianDel Teso Méndez, FélixLindgren, Erikp-LaplacianFinite differenceMean value propertyNonhomogeneous Dirichlet problemViscosity solutionsDynamic programming principleAnálisis matemático1202 Análisis y Análisis FuncionalWe propose a new monotone finite difference discretization for the variational p-Laplace operator, pu = div(|∇u|p−2∇u), and present a convergent numerical scheme for related Dirichlet problems. The resulting nonlinear system is solved using two different methods: one based on Newton-Raphson and one explicit method. Finally, we exhibit some numerical simulations supporting our theoretical results. To the best of our knowledge, this is the first monotone finite difference discretization of the variational p-Laplacian and also the first time that nonhomogeneous problems for this operator can be treated numerically with a finite difference scheme.SpringerUniversidad Complutense de Madrid20222022-01-0120222022-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/71302reponame: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:20.500.14352/713022026-06-02T12:44:21Z
dc.title.none.fl_str_mv A Finite Difference Method for the Variational p-Laplacian
title A Finite Difference Method for the Variational p-Laplacian
spellingShingle A Finite Difference Method for the Variational p-Laplacian
Del Teso Méndez, Félix
p-Laplacian
Finite difference
Mean value property
Nonhomogeneous Dirichlet problem
Viscosity solutions
Dynamic programming principle
Análisis matemático
1202 Análisis y Análisis Funcional
title_short A Finite Difference Method for the Variational p-Laplacian
title_full A Finite Difference Method for the Variational p-Laplacian
title_fullStr A Finite Difference Method for the Variational p-Laplacian
title_full_unstemmed A Finite Difference Method for the Variational p-Laplacian
title_sort A Finite Difference Method for the Variational p-Laplacian
dc.creator.none.fl_str_mv Del Teso Méndez, Félix
Lindgren, Erik
author Del Teso Méndez, Félix
author_facet Del Teso Méndez, Félix
Lindgren, Erik
author_role author
author2 Lindgren, Erik
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv p-Laplacian
Finite difference
Mean value property
Nonhomogeneous Dirichlet problem
Viscosity solutions
Dynamic programming principle
Análisis matemático
1202 Análisis y Análisis Funcional
topic p-Laplacian
Finite difference
Mean value property
Nonhomogeneous Dirichlet problem
Viscosity solutions
Dynamic programming principle
Análisis matemático
1202 Análisis y Análisis Funcional
description We propose a new monotone finite difference discretization for the variational p-Laplace operator, pu = div(|∇u|p−2∇u), and present a convergent numerical scheme for related Dirichlet problems. The resulting nonlinear system is solved using two different methods: one based on Newton-Raphson and one explicit method. Finally, we exhibit some numerical simulations supporting our theoretical results. To the best of our knowledge, this is the first monotone finite difference discretization of the variational p-Laplacian and also the first time that nonhomogeneous problems for this operator can be treated numerically with a finite difference scheme.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01
2022
2022-01-01
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/20.500.14352/71302
url https://hdl.handle.net/20.500.14352/71302
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.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 15.198674

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