On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations

The objective of this paper is to present a framework for the design of discontinuous Galerkin (dG) methods for elliptic problems. The idea is to start from a hybrid formulation of the problem involving as unknowns the main field in the interior of the element domains and its fluxes and traces on th...

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Detalles Bibliográficos
Autores: Codina, Ramon|||0000-0002-7412-778X, Badia, Santiago|||0000-0003-2391-4086
Tipo de recurso: informe técnico
Fecha de publicación:2012
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:2117/16921
Acceso en línea:https://hdl.handle.net/2117/16921
Access Level:acceso abierto
Palabra clave:Galerkin methods
Metode Galerkin discontinu
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
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spelling On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulationsCodina, Ramon|||0000-0002-7412-778XBadia, Santiago|||0000-0003-2391-4086Galerkin methodsMetode Galerkin discontinuÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finitsThe objective of this paper is to present a framework for the design of discontinuous Galerkin (dG) methods for elliptic problems. The idea is to start from a hybrid formulation of the problem involving as unknowns the main field in the interior of the element domains and its fluxes and traces on the element boundaries. Rather than working with this three-field formulation, fluxes are modeled using finite difference expressions and then the traces are determined by imposing continuity of fluxes, although other strategies could be devised. This procedure is applied to four elliptic problems, namely, the convection-diffusion equation (in the diffusion dominated regime), the Stokes problem, the Darcy problem and the Maxwell problem. We justify some well known dG methods with some modifications that in fact allow to improve the performance of the original methods, particularly when the physical properties are discontinuous.20122012-01-0120122012-11-14reporthttp://purl.org/coar/resource_type/c_93fcAOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/16921reponame: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:2117/169212026-05-27T15:37:01Z
dc.title.none.fl_str_mv On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
title On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
spellingShingle On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
Codina, Ramon|||0000-0002-7412-778X
Galerkin methods
Metode Galerkin discontinu
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
title_short On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
title_full On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
title_fullStr On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
title_full_unstemmed On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
title_sort On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
dc.creator.none.fl_str_mv Codina, Ramon|||0000-0002-7412-778X
Badia, Santiago|||0000-0003-2391-4086
author Codina, Ramon|||0000-0002-7412-778X
author_facet Codina, Ramon|||0000-0002-7412-778X
Badia, Santiago|||0000-0003-2391-4086
author_role author
author2 Badia, Santiago|||0000-0003-2391-4086
author2_role author
dc.subject.none.fl_str_mv Galerkin methods
Metode Galerkin discontinu
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
topic Galerkin methods
Metode Galerkin discontinu
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
description The objective of this paper is to present a framework for the design of discontinuous Galerkin (dG) methods for elliptic problems. The idea is to start from a hybrid formulation of the problem involving as unknowns the main field in the interior of the element domains and its fluxes and traces on the element boundaries. Rather than working with this three-field formulation, fluxes are modeled using finite difference expressions and then the traces are determined by imposing continuity of fluxes, although other strategies could be devised. This procedure is applied to four elliptic problems, namely, the convection-diffusion equation (in the diffusion dominated regime), the Stokes problem, the Darcy problem and the Maxwell problem. We justify some well known dG methods with some modifications that in fact allow to improve the performance of the original methods, particularly when the physical properties are discontinuous.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01
2012
2012-11-14
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/16921
url https://hdl.handle.net/2117/16921
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 15,300724

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