Bloch Approximation in Homogenization and Applications

The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions $u^\varepsilon$ of boundary value...

Descripción completa

Detalles Bibliográficos
Autores: Conca Rosende, Carlos, Orive, R., Vanninathan, Muthusamy
Tipo de recurso: artículo
Fecha de publicación:2002
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/57083
Acceso en línea:https://hdl.handle.net/20.500.14352/57083
Access Level:acceso abierto
Palabra clave:517.986.6
517.518
Homogenization
Bloch waves
Correctors
Análisis matemático
1202 Análisis y Análisis Funcional
id ES_35171190c87bbb99735d389aa48c2f4e
oai_identifier_str oai:docta.ucm.es:20.500.14352/57083
network_acronym_str ES
network_name_str España
repository_id_str
spelling Bloch Approximation in Homogenization and ApplicationsConca Rosende, CarlosOrive, R.Vanninathan, Muthusamy517.986.6517.518HomogenizationBloch wavesCorrectorsAnálisis matemático1202 Análisis y Análisis FuncionalThe classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions $u^\varepsilon$ of boundary value problems associated with such operators when the period $\varepsilon>0$ of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as $\varepsilon\to 0$ towards the homogenized solution was furnished using Bloch wave decomposition. Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution $u^\varepsilon$. We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to capture the oscillations of the solution in a sharper way. The present approach sheds new light and offers an alternative for viewing classical results.Society for Industrial and Applied MathematicsUniversidad Complutense de Madrid20022002-04-1120022002-04-11journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/57083reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/570832026-06-02T12:44:21Z
dc.title.none.fl_str_mv Bloch Approximation in Homogenization and Applications
title Bloch Approximation in Homogenization and Applications
spellingShingle Bloch Approximation in Homogenization and Applications
Conca Rosende, Carlos
517.986.6
517.518
Homogenization
Bloch waves
Correctors
Análisis matemático
1202 Análisis y Análisis Funcional
title_short Bloch Approximation in Homogenization and Applications
title_full Bloch Approximation in Homogenization and Applications
title_fullStr Bloch Approximation in Homogenization and Applications
title_full_unstemmed Bloch Approximation in Homogenization and Applications
title_sort Bloch Approximation in Homogenization and Applications
dc.creator.none.fl_str_mv Conca Rosende, Carlos
Orive, R.
Vanninathan, Muthusamy
author Conca Rosende, Carlos
author_facet Conca Rosende, Carlos
Orive, R.
Vanninathan, Muthusamy
author_role author
author2 Orive, R.
Vanninathan, Muthusamy
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.986.6
517.518
Homogenization
Bloch waves
Correctors
Análisis matemático
1202 Análisis y Análisis Funcional
topic 517.986.6
517.518
Homogenization
Bloch waves
Correctors
Análisis matemático
1202 Análisis y Análisis Funcional
description The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions $u^\varepsilon$ of boundary value problems associated with such operators when the period $\varepsilon>0$ of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as $\varepsilon\to 0$ towards the homogenized solution was furnished using Bloch wave decomposition. Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution $u^\varepsilon$. We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to capture the oscillations of the solution in a sharper way. The present approach sheds new light and offers an alternative for viewing classical results.
publishDate 2002
dc.date.none.fl_str_mv 2002
2002-04-11
2002
2002-04-11
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/20.500.14352/57083
url https://hdl.handle.net/20.500.14352/57083
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
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
_version_ 1869405859366305792
score 15,300724

Similares en LA Referencia