Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , |
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=S2179-84512017000200287 |
Resumo: | ABSTRACT In this work we present an efficient Galerkin least squares finite element scheme to simulate the Burgers’ equation on the whole real line and subjected to initial conditions with compact support. The numerical simulations are performed by considering a sequence of auxiliary spatially dimensionless Dirichlet’s problems parameterized by its numerical support K ˜. Gaining advantage from the well-known convective-diffusive effects of the Burgers’ equation, computations start by choosing K ˜ so it contains the support of the initial condition and, as solution diffuses out, K ˜ is increased appropriately. By direct comparisons between numerical and analytic solutions and its asymptotic behavior, we conclude that the proposed scheme is accurate even for large times, and it can be applied to numerically investigate properties of this and similar equations on unbounded domains. |
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Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real LineBurgers’ equation on the real lineGalerkin least squares finite element methodasymptotic propertiesABSTRACT In this work we present an efficient Galerkin least squares finite element scheme to simulate the Burgers’ equation on the whole real line and subjected to initial conditions with compact support. The numerical simulations are performed by considering a sequence of auxiliary spatially dimensionless Dirichlet’s problems parameterized by its numerical support K ˜. Gaining advantage from the well-known convective-diffusive effects of the Burgers’ equation, computations start by choosing K ˜ so it contains the support of the initial condition and, as solution diffuses out, K ˜ is increased appropriately. By direct comparisons between numerical and analytic solutions and its asymptotic behavior, we conclude that the proposed scheme is accurate even for large times, and it can be applied to numerically investigate properties of this and similar equations on unbounded domains.Sociedade Brasileira de Matemática Aplicada e Computacional2017-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000200287TEMA (São Carlos) v.18 n.2 2017reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2017.018.02.0287info:eu-repo/semantics/openAccessKONZEN,P.H.A.AZEVEDO,F.S.SAUTER,E.ZINGANO,P.R.A.eng2017-09-14T00:00:00Zoai:scielo:S2179-84512017000200287Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2017-09-14T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse |
dc.title.none.fl_str_mv |
Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line |
title |
Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line |
spellingShingle |
Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line KONZEN,P.H.A. Burgers’ equation on the real line Galerkin least squares finite element method asymptotic properties |
title_short |
Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line |
title_full |
Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line |
title_fullStr |
Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line |
title_full_unstemmed |
Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line |
title_sort |
Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line |
author |
KONZEN,P.H.A. |
author_facet |
KONZEN,P.H.A. AZEVEDO,F.S. SAUTER,E. ZINGANO,P.R.A. |
author_role |
author |
author2 |
AZEVEDO,F.S. SAUTER,E. ZINGANO,P.R.A. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
KONZEN,P.H.A. AZEVEDO,F.S. SAUTER,E. ZINGANO,P.R.A. |
dc.subject.por.fl_str_mv |
Burgers’ equation on the real line Galerkin least squares finite element method asymptotic properties |
topic |
Burgers’ equation on the real line Galerkin least squares finite element method asymptotic properties |
description |
ABSTRACT In this work we present an efficient Galerkin least squares finite element scheme to simulate the Burgers’ equation on the whole real line and subjected to initial conditions with compact support. The numerical simulations are performed by considering a sequence of auxiliary spatially dimensionless Dirichlet’s problems parameterized by its numerical support K ˜. Gaining advantage from the well-known convective-diffusive effects of the Burgers’ equation, computations start by choosing K ˜ so it contains the support of the initial condition and, as solution diffuses out, K ˜ is increased appropriately. By direct comparisons between numerical and analytic solutions and its asymptotic behavior, we conclude that the proposed scheme is accurate even for large times, and it can be applied to numerically investigate properties of this and similar equations on unbounded domains. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-08-01 |
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=S2179-84512017000200287 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000200287 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.5540/tema.2017.018.02.0287 |
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.18 n.2 2017 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 |
instacron_str |
SBMAC |
institution |
SBMAC |
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 |
_version_ |
1752122220219465728 |