Convergence of an adaptive Kačanov FEM for quasi-linear problems

Autores
Garau, Eduardo Mario; Morin, Pedro; Zuppa, Carlos
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Kačanov iteration and a mesh adaptation step is performed after each linear solve. The method is thus inexact because we do not solve the discrete nonlinear problems exactly, but rather perform one iteration of a fixed point method (Kačanov), using the approximation of the previous mesh as an initial guess. The convergence of the method is proved for any reasonable marking strategy and starting from any initial mesh. We conclude with some numerical experiments that illustrate the theory.
Fil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Zuppa, Carlos. Universidad Nacional de San Luis; Argentina
Materia
Adaptive Finite Element Methods
Convergence
Nonlinear Stationary Conservation Laws
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:11336/75181
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Convergence of an adaptive Kačanov FEM for quasi-linear problemsGarau, Eduardo MarioMorin, PedroZuppa, CarlosAdaptive Finite Element MethodsConvergenceNonlinear Stationary Conservation Lawshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Kačanov iteration and a mesh adaptation step is performed after each linear solve. The method is thus inexact because we do not solve the discrete nonlinear problems exactly, but rather perform one iteration of a fixed point method (Kačanov), using the approximation of the previous mesh as an initial guess. The convergence of the method is proved for any reasonable marking strategy and starting from any initial mesh. We conclude with some numerical experiments that illustrate the theory.Fil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Zuppa, Carlos. Universidad Nacional de San Luis; ArgentinaElsevier Science2011-04info: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/11336/75181Garau, Eduardo Mario; Morin, Pedro; Zuppa, Carlos; Convergence of an adaptive Kačanov FEM for quasi-linear problems; Elsevier Science; Applied Numerical Mathematics; 61; 4; 4-2011; 512-5290168-9274CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.apnum.2010.12.001info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:58:37Zoai:ri.conicet.gov.ar:11336/75181instacron: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 09:58:37.739CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Convergence of an adaptive Kačanov FEM for quasi-linear problems
title Convergence of an adaptive Kačanov FEM for quasi-linear problems
spellingShingle Convergence of an adaptive Kačanov FEM for quasi-linear problems
Garau, Eduardo Mario
Adaptive Finite Element Methods
Convergence
Nonlinear Stationary Conservation Laws
title_short Convergence of an adaptive Kačanov FEM for quasi-linear problems
title_full Convergence of an adaptive Kačanov FEM for quasi-linear problems
title_fullStr Convergence of an adaptive Kačanov FEM for quasi-linear problems
title_full_unstemmed Convergence of an adaptive Kačanov FEM for quasi-linear problems
title_sort Convergence of an adaptive Kačanov FEM for quasi-linear problems
dc.creator.none.fl_str_mv Garau, Eduardo Mario
Morin, Pedro
Zuppa, Carlos
author Garau, Eduardo Mario
author_facet Garau, Eduardo Mario
Morin, Pedro
Zuppa, Carlos
author_role author
author2 Morin, Pedro
Zuppa, Carlos
author2_role author
author
dc.subject.none.fl_str_mv Adaptive Finite Element Methods
Convergence
Nonlinear Stationary Conservation Laws
topic Adaptive Finite Element Methods
Convergence
Nonlinear Stationary Conservation Laws
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Kačanov iteration and a mesh adaptation step is performed after each linear solve. The method is thus inexact because we do not solve the discrete nonlinear problems exactly, but rather perform one iteration of a fixed point method (Kačanov), using the approximation of the previous mesh as an initial guess. The convergence of the method is proved for any reasonable marking strategy and starting from any initial mesh. We conclude with some numerical experiments that illustrate the theory.
Fil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Morin, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Zuppa, Carlos. Universidad Nacional de San Luis; Argentina
description We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Kačanov iteration and a mesh adaptation step is performed after each linear solve. The method is thus inexact because we do not solve the discrete nonlinear problems exactly, but rather perform one iteration of a fixed point method (Kačanov), using the approximation of the previous mesh as an initial guess. The convergence of the method is proved for any reasonable marking strategy and starting from any initial mesh. We conclude with some numerical experiments that illustrate the theory.
publishDate 2011
dc.date.none.fl_str_mv 2011-04
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/11336/75181
Garau, Eduardo Mario; Morin, Pedro; Zuppa, Carlos; Convergence of an adaptive Kačanov FEM for quasi-linear problems; Elsevier Science; Applied Numerical Mathematics; 61; 4; 4-2011; 512-529
0168-9274
CONICET Digital
CONICET
url http://hdl.handle.net/11336/75181
identifier_str_mv Garau, Eduardo Mario; Morin, Pedro; Zuppa, Carlos; Convergence of an adaptive Kačanov FEM for quasi-linear problems; Elsevier Science; Applied Numerical Mathematics; 61; 4; 4-2011; 512-529
0168-9274
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.apnum.2010.12.001
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 Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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
_version_ 1842269531419967488
score 13.13397

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