Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations

A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov–Galerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FO...

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Detalhes bibliográficos
Autores: John, Volker, Moreau, Baptiste, Novo Martín, Julia
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/717681
Acesso em linha:http://hdl.handle.net/10486/717681
https://dx.doi.org/10.1016/j.camwa.2022.07.017
Access Level:acceso abierto
Palavra-chave:A posteriori error estimation
convection-diffusion-reaction equations
convection-dominated regime
error analysis
SUPG-ROM method
Matemáticas
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spelling Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equationsJohn, VolkerMoreau, BaptisteNovo Martín, JuliaA posteriori error estimationconvection-diffusion-reaction equationsconvection-dominated regimeerror analysisSUPG-ROM methodMatemáticasA reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov–Galerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FOM) and the ROM simulations. The asymptotic choice of the stabilization parameter for the SUPG-ROM is done as proposed in the literature. This paper presents a finite element convergence analysis of the SUPG-ROM method for errors in different norms. The constants in the error bounds are uniform with respect to small diffusion coefficients. An approach for a posteriori error estimation is discussed. Numerical studies illustrate the performance of the SUPG-ROM methodThe research of Julia Novo was supported by Spanish MINECO under grants PID2019-104141GB-I00 and VA169P20 (Junta de Castilla y Leon, ES)ElsevierDepartamento de MatemáticasFacultad de Ciencias20222022-09-15research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/717681https://dx.doi.org/10.1016/j.camwa.2022.07.017reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7176812026-06-23T12:46:27Z
dc.title.none.fl_str_mv Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
title Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
spellingShingle Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
John, Volker
A posteriori error estimation
convection-diffusion-reaction equations
convection-dominated regime
error analysis
SUPG-ROM method
Matemáticas
title_short Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
title_full Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
title_fullStr Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
title_full_unstemmed Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
title_sort Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
dc.creator.none.fl_str_mv John, Volker
Moreau, Baptiste
Novo Martín, Julia
author John, Volker
author_facet John, Volker
Moreau, Baptiste
Novo Martín, Julia
author_role author
author2 Moreau, Baptiste
Novo Martín, Julia
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv A posteriori error estimation
convection-diffusion-reaction equations
convection-dominated regime
error analysis
SUPG-ROM method
Matemáticas
topic A posteriori error estimation
convection-diffusion-reaction equations
convection-dominated regime
error analysis
SUPG-ROM method
Matemáticas
description A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov–Galerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FOM) and the ROM simulations. The asymptotic choice of the stabilization parameter for the SUPG-ROM is done as proposed in the literature. This paper presents a finite element convergence analysis of the SUPG-ROM method for errors in different norms. The constants in the error bounds are uniform with respect to small diffusion coefficients. An approach for a posteriori error estimation is discussed. Numerical studies illustrate the performance of the SUPG-ROM method
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-09-15
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/717681
https://dx.doi.org/10.1016/j.camwa.2022.07.017
url http://hdl.handle.net/10486/717681
https://dx.doi.org/10.1016/j.camwa.2022.07.017
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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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