A weighted mass explicit scheme for convection-diffusion equations

Detalhes bibliográficos
Autor(a) principal: Ruas,Vitoriano
Data de Publicação: 2012
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022012000300004
Resumo: An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method's weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we study some techniques for choosing the weights that guarantee the convergence of the scheme with optimal order in the space-time maximum norm, as both discretisation parameters tend to zero. Mathematical subject classification: Primary: 65M60; Secondary: 76Rxx.
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spelling A weighted mass explicit scheme for convection-diffusion equationsConvection-diffusionconvergenceexplicit schemefinite elementspiecewise lineartime-dependentweighted massAn explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method's weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we study some techniques for choosing the weights that guarantee the convergence of the scheme with optimal order in the space-time maximum norm, as both discretisation parameters tend to zero. Mathematical subject classification: Primary: 65M60; Secondary: 76Rxx.Sociedade Brasileira de Matemática Aplicada e Computacional2012-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022012000300004Computational & Applied Mathematics v.31 n.3 2012reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022012000300004info:eu-repo/semantics/openAccessRuas,Vitorianoeng2012-11-28T00:00:00Zoai:scielo:S1807-03022012000300004Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2012-11-28T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv A weighted mass explicit scheme for convection-diffusion equations
title A weighted mass explicit scheme for convection-diffusion equations
spellingShingle A weighted mass explicit scheme for convection-diffusion equations
Ruas,Vitoriano
Convection-diffusion
convergence
explicit scheme
finite elements
piecewise linear
time-dependent
weighted mass
title_short A weighted mass explicit scheme for convection-diffusion equations
title_full A weighted mass explicit scheme for convection-diffusion equations
title_fullStr A weighted mass explicit scheme for convection-diffusion equations
title_full_unstemmed A weighted mass explicit scheme for convection-diffusion equations
title_sort A weighted mass explicit scheme for convection-diffusion equations
author Ruas,Vitoriano
author_facet Ruas,Vitoriano
author_role author
dc.contributor.author.fl_str_mv Ruas,Vitoriano
dc.subject.por.fl_str_mv Convection-diffusion
convergence
explicit scheme
finite elements
piecewise linear
time-dependent
weighted mass
topic Convection-diffusion
convergence
explicit scheme
finite elements
piecewise linear
time-dependent
weighted mass
description An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method's weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we study some techniques for choosing the weights that guarantee the convergence of the scheme with optimal order in the space-time maximum norm, as both discretisation parameters tend to zero. Mathematical subject classification: Primary: 65M60; Secondary: 76Rxx.
publishDate 2012
dc.date.none.fl_str_mv 2012-01-01
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=S1807-03022012000300004
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022012000300004
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022012000300004
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 Computational & Applied Mathematics v.31 n.3 2012
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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