Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and...

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Detalles Bibliográficos
Autores: Rojas, S., Pardo, D., Behnoudfare, P., Calo, V. M.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1261
Acceso en línea:http://hdl.handle.net/20.500.11824/1261
Access Level:acceso abierto
Palabra clave:goal-oriented adaptivity
stabilized finite elements
residual minimization
inf-sup stability
discontinuous Galerkin
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spelling Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin normRojas, S.Pardo, D.Behnoudfare, P.Calo, V. M.goal-oriented adaptivitystabilized finite elementsresidual minimizationinf-sup stabilitydiscontinuous GalerkinWe propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and a residual projection onto a broken polynomial space, which is a robust error estimator to minimize the discrete energy norm via automatic mesh refinement. In this work, we propose and analyze a goal-oriented adaptive algorithm for this stable residual minimization. We solve the primal and adjoint problems considering the same saddle-point formulation and different right-hand sides. By solving a third stable problem, we obtain two efficient error estimates to guide goal oriented adaptivity. We illustrate the performance of this goal-oriented adaptive strategy on advection-diffusion reaction problems.202120212021info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1261reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/abs/pii/S0045782521000220info:eu-repo/grantAgreement/EC/H2020/777778info:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108111RB-I00info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/12612026-06-19T12:47:47Z
dc.title.none.fl_str_mv Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
title Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
spellingShingle Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
Rojas, S.
goal-oriented adaptivity
stabilized finite elements
residual minimization
inf-sup stability
discontinuous Galerkin
title_short Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
title_full Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
title_fullStr Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
title_full_unstemmed Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
title_sort Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
dc.creator.none.fl_str_mv Rojas, S.
Pardo, D.
Behnoudfare, P.
Calo, V. M.
author Rojas, S.
author_facet Rojas, S.
Pardo, D.
Behnoudfare, P.
Calo, V. M.
author_role author
author2 Pardo, D.
Behnoudfare, P.
Calo, V. M.
author2_role author
author
author
dc.subject.none.fl_str_mv goal-oriented adaptivity
stabilized finite elements
residual minimization
inf-sup stability
discontinuous Galerkin
topic goal-oriented adaptivity
stabilized finite elements
residual minimization
inf-sup stability
discontinuous Galerkin
description We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and a residual projection onto a broken polynomial space, which is a robust error estimator to minimize the discrete energy norm via automatic mesh refinement. In this work, we propose and analyze a goal-oriented adaptive algorithm for this stable residual minimization. We solve the primal and adjoint problems considering the same saddle-point formulation and different right-hand sides. By solving a third stable problem, we obtain two efficient error estimates to guide goal oriented adaptivity. We illustrate the performance of this goal-oriented adaptive strategy on advection-diffusion reaction problems.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1261
url http://hdl.handle.net/20.500.11824/1261
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/abs/pii/S0045782521000220
info:eu-repo/grantAgreement/EC/H2020/777778
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108111RB-I00
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
repository.name.fl_str_mv
repository.mail.fl_str_mv
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