SUPG-based stabilization using a separated representations approach

We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG sc...

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Detalles Bibliográficos
Autores: González, D., Debeugny, L., Cueto, E., Chinesta, F., Díez, Pedro|||0000-0001-6464-6407, Huerta, Antonio|||0000-0003-4198-3798
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/10251
Acceso en línea:https://hdl.handle.net/2117/10251
https://dx.doi.org/10.1007/s12289-010-0909-7
Access Level:acceso abierto
Palabra clave:Numerical methods and algorithms
Finite element method
Differential equations, Partial
Anàlisi numèrica
Elements finits, Mètode dels
Equacions diferencials parcials
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
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repository_id_str
spelling SUPG-based stabilization using a separated representations approachGonzález, D.Debeugny, L.Cueto, E.Chinesta, F.Díez, Pedro|||0000-0001-6464-6407Huerta, Antonio|||0000-0003-4198-3798Numerical methods and algorithmsFinite element methodDifferential equations, PartialAnàlisi numèricaElements finits, Mètode delsEquacions diferencials parcialsÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèricsWe have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG schemes produces a consistent stabilization adding a parameter to all the terms of the equation (not only the convective one). SUPG obtains an exact solution for problems in 1D, nevertheless, a generalization does not exist for elements of high order or for any system of convection-diffusion equations. We introduce in this paper a method that achieves stabilization in the context of Proper Generalzied Decomposition (PGD). This class of approximations use a representation of the solution by means of the sum of a finite number of terms of separable functions. Thus it is possible to use the technique of separation of variables in the context of problems of convection-diffusion that will lead to a sequence of problems in 1D where the parameter of stabilization is well known.20102010-04-0120102010-11-11journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/10251https://dx.doi.org/10.1007/s12289-010-0909-7reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/102512026-05-27T15:37:01Z
dc.title.none.fl_str_mv SUPG-based stabilization using a separated representations approach
title SUPG-based stabilization using a separated representations approach
spellingShingle SUPG-based stabilization using a separated representations approach
González, D.
Numerical methods and algorithms
Finite element method
Differential equations, Partial
Anàlisi numèrica
Elements finits, Mètode dels
Equacions diferencials parcials
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
title_short SUPG-based stabilization using a separated representations approach
title_full SUPG-based stabilization using a separated representations approach
title_fullStr SUPG-based stabilization using a separated representations approach
title_full_unstemmed SUPG-based stabilization using a separated representations approach
title_sort SUPG-based stabilization using a separated representations approach
dc.creator.none.fl_str_mv González, D.
Debeugny, L.
Cueto, E.
Chinesta, F.
Díez, Pedro|||0000-0001-6464-6407
Huerta, Antonio|||0000-0003-4198-3798
author González, D.
author_facet González, D.
Debeugny, L.
Cueto, E.
Chinesta, F.
Díez, Pedro|||0000-0001-6464-6407
Huerta, Antonio|||0000-0003-4198-3798
author_role author
author2 Debeugny, L.
Cueto, E.
Chinesta, F.
Díez, Pedro|||0000-0001-6464-6407
Huerta, Antonio|||0000-0003-4198-3798
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Numerical methods and algorithms
Finite element method
Differential equations, Partial
Anàlisi numèrica
Elements finits, Mètode dels
Equacions diferencials parcials
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
topic Numerical methods and algorithms
Finite element method
Differential equations, Partial
Anàlisi numèrica
Elements finits, Mètode dels
Equacions diferencials parcials
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
description We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG schemes produces a consistent stabilization adding a parameter to all the terms of the equation (not only the convective one). SUPG obtains an exact solution for problems in 1D, nevertheless, a generalization does not exist for elements of high order or for any system of convection-diffusion equations. We introduce in this paper a method that achieves stabilization in the context of Proper Generalzied Decomposition (PGD). This class of approximations use a representation of the solution by means of the sum of a finite number of terms of separable functions. Thus it is possible to use the technique of separation of variables in the context of problems of convection-diffusion that will lead to a sequence of problems in 1D where the parameter of stabilization is well known.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-04-01
2010
2010-11-11
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/10251
https://dx.doi.org/10.1007/s12289-010-0909-7
url https://hdl.handle.net/2117/10251
https://dx.doi.org/10.1007/s12289-010-0909-7
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.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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