An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method

Autores
Bustinza, Rommel; Lombardi, Ariel Luis; Solano, Manuel
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper deals with the a priori error analysis for a convection-dominated diffusion 2D problem, when applying the HDG method on a family of anisotropic triangulations. It is known that in this case, boundary or interior layers may appear. Therefore, it is important to resolve these layers in order to recover, if possible, the expected order of approximation. In this work, we extend the use of HDG method on anisotropic meshes. To this end, some assumptions need to be asked to the stabilization parameter, as well as to the family of triangulations. In this context, when the discrete local spaces are polynomials of degree k ≥ 0, this approach is able to recover an order of convergence k + 1 2 in L 2 for all the variables. Numerical examples confirm our theoretical results.
Fil: Bustinza, Rommel. Universidad de Concepción; Chile
Fil: Lombardi, Ariel Luis. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Solano, Manuel. Universidad de Concepción; Chile
Materia
ANISOTROPIC MESHES
CONVECTION-DOMINATED DIFFUSION PROBLEM
HYBRIDIZABLE DISCONTINUOUS GALERKIN
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/154240
Acceder
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network_name_str CONICET Digital (CONICET)
spelling An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG methodBustinza, RommelLombardi, Ariel LuisSolano, ManuelANISOTROPIC MESHESCONVECTION-DOMINATED DIFFUSION PROBLEMHYBRIDIZABLE DISCONTINUOUS GALERKINhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper deals with the a priori error analysis for a convection-dominated diffusion 2D problem, when applying the HDG method on a family of anisotropic triangulations. It is known that in this case, boundary or interior layers may appear. Therefore, it is important to resolve these layers in order to recover, if possible, the expected order of approximation. In this work, we extend the use of HDG method on anisotropic meshes. To this end, some assumptions need to be asked to the stabilization parameter, as well as to the family of triangulations. In this context, when the discrete local spaces are polynomials of degree k ≥ 0, this approach is able to recover an order of convergence k + 1 2 in L 2 for all the variables. Numerical examples confirm our theoretical results.Fil: Bustinza, Rommel. Universidad de Concepción; ChileFil: Lombardi, Ariel Luis. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Solano, Manuel. Universidad de Concepción; ChileElsevier Science SA2019-03-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/154240Bustinza, Rommel; Lombardi, Ariel Luis; Solano, Manuel; An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method; Elsevier Science SA; Computer Methods in Applied Mechanics and Engineering; 345; 1-3-2019; 382-4010045-78251879-2138CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0045782518305656info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2018.11.010info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:25:54Zoai:ri.conicet.gov.ar:11336/154240instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:25:54.612CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method
title An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method
spellingShingle An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method
Bustinza, Rommel
ANISOTROPIC MESHES
CONVECTION-DOMINATED DIFFUSION PROBLEM
HYBRIDIZABLE DISCONTINUOUS GALERKIN
title_short An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method
title_full An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method
title_fullStr An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method
title_full_unstemmed An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method
title_sort An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method
dc.creator.none.fl_str_mv Bustinza, Rommel
Lombardi, Ariel Luis
Solano, Manuel
author Bustinza, Rommel
author_facet Bustinza, Rommel
Lombardi, Ariel Luis
Solano, Manuel
author_role author
author2 Lombardi, Ariel Luis
Solano, Manuel
author2_role author
author
dc.subject.none.fl_str_mv ANISOTROPIC MESHES
CONVECTION-DOMINATED DIFFUSION PROBLEM
HYBRIDIZABLE DISCONTINUOUS GALERKIN
topic ANISOTROPIC MESHES
CONVECTION-DOMINATED DIFFUSION PROBLEM
HYBRIDIZABLE DISCONTINUOUS GALERKIN
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper deals with the a priori error analysis for a convection-dominated diffusion 2D problem, when applying the HDG method on a family of anisotropic triangulations. It is known that in this case, boundary or interior layers may appear. Therefore, it is important to resolve these layers in order to recover, if possible, the expected order of approximation. In this work, we extend the use of HDG method on anisotropic meshes. To this end, some assumptions need to be asked to the stabilization parameter, as well as to the family of triangulations. In this context, when the discrete local spaces are polynomials of degree k ≥ 0, this approach is able to recover an order of convergence k + 1 2 in L 2 for all the variables. Numerical examples confirm our theoretical results.
Fil: Bustinza, Rommel. Universidad de Concepción; Chile
Fil: Lombardi, Ariel Luis. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Solano, Manuel. Universidad de Concepción; Chile
description This paper deals with the a priori error analysis for a convection-dominated diffusion 2D problem, when applying the HDG method on a family of anisotropic triangulations. It is known that in this case, boundary or interior layers may appear. Therefore, it is important to resolve these layers in order to recover, if possible, the expected order of approximation. In this work, we extend the use of HDG method on anisotropic meshes. To this end, some assumptions need to be asked to the stabilization parameter, as well as to the family of triangulations. In this context, when the discrete local spaces are polynomials of degree k ≥ 0, this approach is able to recover an order of convergence k + 1 2 in L 2 for all the variables. Numerical examples confirm our theoretical results.
publishDate 2019
dc.date.none.fl_str_mv 2019-03-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/154240
Bustinza, Rommel; Lombardi, Ariel Luis; Solano, Manuel; An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method; Elsevier Science SA; Computer Methods in Applied Mechanics and Engineering; 345; 1-3-2019; 382-401
0045-7825
1879-2138
CONICET Digital
CONICET
url http://hdl.handle.net/11336/154240
identifier_str_mv Bustinza, Rommel; Lombardi, Ariel Luis; Solano, Manuel; An anisotropic a priori error analysis for a convection-dominated diffusion problem using the HDG method; Elsevier Science SA; Computer Methods in Applied Mechanics and Engineering; 345; 1-3-2019; 382-401
0045-7825
1879-2138
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0045782518305656
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2018.11.010
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science SA
publisher.none.fl_str_mv Elsevier Science SA
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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