Homogenization of a Continuously Microperiodic Multidimensional Medium

Detalhes bibliográficos
Autor(a) principal: LIMA,M. P.
Data de Publicação: 2018
Outros Autores: PÉREZ-FERNÁNDEZ,L. D., BRAVO-CASTILLERO,J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100015
Resumo: ABSTRACT The asymptotic homogenization method is applied to obtain formal asymptotic solution and the homogenized solution of a Dirichlet boundary-value problem for an elliptic equation with rapidly oscillating coefficients. The proximity of the formal asymptotic solution and the homogenized solution to the exact solution is proved, which provides the mathematical justification of the homogenization process. Preservation of the symmetry and positive-definiteness of the effective coefficient in the homogenized problem is also proved. An example is presented in order to illustrate the theoretical results.
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spelling Homogenization of a Continuously Microperiodic Multidimensional MediumMicroperiodic mediumeffective behaviorasymptotic homogenization methodABSTRACT The asymptotic homogenization method is applied to obtain formal asymptotic solution and the homogenized solution of a Dirichlet boundary-value problem for an elliptic equation with rapidly oscillating coefficients. The proximity of the formal asymptotic solution and the homogenized solution to the exact solution is proved, which provides the mathematical justification of the homogenization process. Preservation of the symmetry and positive-definiteness of the effective coefficient in the homogenized problem is also proved. An example is presented in order to illustrate the theoretical results.Sociedade Brasileira de Matemática Aplicada e Computacional2018-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100015TEMA (São Carlos) v.19 n.1 2018reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2018.019.01.0015info:eu-repo/semantics/openAccessLIMA,M. P.PÉREZ-FERNÁNDEZ,L. D.BRAVO-CASTILLERO,J.eng2018-05-29T00:00:00Zoai:scielo:S2179-84512018000100015Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-05-29T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Homogenization of a Continuously Microperiodic Multidimensional Medium
title Homogenization of a Continuously Microperiodic Multidimensional Medium
spellingShingle Homogenization of a Continuously Microperiodic Multidimensional Medium
LIMA,M. P.
Microperiodic medium
effective behavior
asymptotic homogenization method
title_short Homogenization of a Continuously Microperiodic Multidimensional Medium
title_full Homogenization of a Continuously Microperiodic Multidimensional Medium
title_fullStr Homogenization of a Continuously Microperiodic Multidimensional Medium
title_full_unstemmed Homogenization of a Continuously Microperiodic Multidimensional Medium
title_sort Homogenization of a Continuously Microperiodic Multidimensional Medium
author LIMA,M. P.
author_facet LIMA,M. P.
PÉREZ-FERNÁNDEZ,L. D.
BRAVO-CASTILLERO,J.
author_role author
author2 PÉREZ-FERNÁNDEZ,L. D.
BRAVO-CASTILLERO,J.
author2_role author
author
dc.contributor.author.fl_str_mv LIMA,M. P.
PÉREZ-FERNÁNDEZ,L. D.
BRAVO-CASTILLERO,J.
dc.subject.por.fl_str_mv Microperiodic medium
effective behavior
asymptotic homogenization method
topic Microperiodic medium
effective behavior
asymptotic homogenization method
description ABSTRACT The asymptotic homogenization method is applied to obtain formal asymptotic solution and the homogenized solution of a Dirichlet boundary-value problem for an elliptic equation with rapidly oscillating coefficients. The proximity of the formal asymptotic solution and the homogenized solution to the exact solution is proved, which provides the mathematical justification of the homogenization process. Preservation of the symmetry and positive-definiteness of the effective coefficient in the homogenized problem is also proved. An example is presented in order to illustrate the theoretical results.
publishDate 2018
dc.date.none.fl_str_mv 2018-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100015
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100015
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2018.019.01.0015
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.19 n.1 2018
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
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reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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