Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients

In this work we review some recent results on approximation of solutions of elliptic problems with high-contrast coefficients. In particular, we detail the derivation of asymptotic expansions for the solution in terms of the high-contrast of the cofficients. We consider the case of high-contrast ell...

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Autores:
Poveda Cuevas, Leonardo Andrés
Tipo de recurso:
Article of journal
Fecha de publicación:
2014
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/61901
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/61901
http://bdigital.unal.edu.co/60713/
Palabra clave:
51 Matemáticas / Mathematics
Elliptic equations
high-contrast coe_cients
asymptotic expansions.
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/61901
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repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Poveda Cuevas, Leonardo Andrés424f294c-d7bc-4c82-804d-5435006daf723002019-07-02T20:47:09Z2019-07-02T20:47:09Z2014-07-01ISSN: 2357-6529https://repositorio.unal.edu.co/handle/unal/61901http://bdigital.unal.edu.co/60713/In this work we review some recent results on approximation of solutions of elliptic problems with high-contrast coefficients. In particular, we detail the derivation of asymptotic expansions for the solution in terms of the high-contrast of the cofficients. We consider the case of high-contrast elliptic equations and we present the case of only one high-contrast inclusion. The case of more inclusions follows similarly. In order to simplify the presentation we consider first the one dimensional case so no further complicated requirements regarding the computation of two or higher dimensional integrals are needed. We review the case of two-dimensional problems and give some numerical examples.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticashttps://revistas.unal.edu.co/index.php/bolma/article/view/48100Universidad Nacional de Colombia Revistas electrónicas UN Boletín de MatemáticasBoletín de MatemáticasPoveda Cuevas, Leonardo Andrés (2014) Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients. Boletín de Matemáticas, 21 (2). pp. 99-124. ISSN 2357-652951 Matemáticas / MathematicsElliptic equationshigh-contrast coe_cientsasymptotic expansions.Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficientsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL48100-235159-1-PB.pdfapplication/pdf800789https://repositorio.unal.edu.co/bitstream/unal/61901/1/48100-235159-1-PB.pdf6dce0eb600038eab6e248f57c14063cfMD51THUMBNAIL48100-235159-1-PB.pdf.jpg48100-235159-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5851https://repositorio.unal.edu.co/bitstream/unal/61901/2/48100-235159-1-PB.pdf.jpgeda89d168d44a91d984c1c3ce553e413MD52unal/61901oai:repositorio.unal.edu.co:unal/619012024-04-20 23:26:20.325Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients
title Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients
spellingShingle Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients
51 Matemáticas / Mathematics
Elliptic equations
high-contrast coe_cients
asymptotic expansions.
title_short Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients
title_full Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients
title_fullStr Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients
title_full_unstemmed Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients
title_sort Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients
dc.creator.fl_str_mv Poveda Cuevas, Leonardo Andrés
dc.contributor.author.spa.fl_str_mv Poveda Cuevas, Leonardo Andrés
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Elliptic equations
high-contrast coe_cients
asymptotic expansions.
dc.subject.proposal.spa.fl_str_mv Elliptic equations
high-contrast coe_cients
asymptotic expansions.
description In this work we review some recent results on approximation of solutions of elliptic problems with high-contrast coefficients. In particular, we detail the derivation of asymptotic expansions for the solution in terms of the high-contrast of the cofficients. We consider the case of high-contrast elliptic equations and we present the case of only one high-contrast inclusion. The case of more inclusions follows similarly. In order to simplify the presentation we consider first the one dimensional case so no further complicated requirements regarding the computation of two or higher dimensional integrals are needed. We review the case of two-dimensional problems and give some numerical examples.
publishDate 2014
dc.date.issued.spa.fl_str_mv 2014-07-01
dc.date.accessioned.spa.fl_str_mv 2019-07-02T20:47:09Z
dc.date.available.spa.fl_str_mv 2019-07-02T20:47:09Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv ISSN: 2357-6529
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/61901
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/60713/
identifier_str_mv ISSN: 2357-6529
url https://repositorio.unal.edu.co/handle/unal/61901
http://bdigital.unal.edu.co/60713/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/bolma/article/view/48100
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Boletín de Matemáticas
Boletín de Matemáticas
dc.relation.references.spa.fl_str_mv Poveda Cuevas, Leonardo Andrés (2014) Using weak forms to derive asymptotic expansions of elliptic equations with high-contrast cofficients. Boletín de Matemáticas, 21 (2). pp. 99-124. ISSN 2357-6529
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/61901/1/48100-235159-1-PB.pdf
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