A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems

This work extends an automatic energy-norm hp-adaptive strategy based on performing quasi-optimal unrefinements to the case of non-elliptic problems and goal-oriented adaptivity. The proposed approach employs a multi-level hierarchical data structure and alternates global h- and p-refinements with a...

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Autores: Caro Gutiérrez, Felipe Vinicio, Darrigrand, Vincent, Alvarez Aramberri, Julen, Alberdi Celaya, Elisabete, Pardo Zubiaur, David
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/77539
Acceso en línea:http://hdl.handle.net/10810/77539
Access Level:acceso abierto
Palabra clave:goal-oriented adaptivity
hp-adaptivity
finite element method
unrefinements
non-elliptic problems
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spelling A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problemsCaro Gutiérrez, Felipe VinicioDarrigrand, VincentAlvarez Aramberri, JulenAlberdi Celaya, ElisabetePardo Zubiaur, Davidgoal-oriented adaptivityhp-adaptivityfinite element methodunrefinementsnon-elliptic problemsThis work extends an automatic energy-norm hp-adaptive strategy based on performing quasi-optimal unrefinements to the case of non-elliptic problems and goal-oriented adaptivity. The proposed approach employs a multi-level hierarchical data structure and alternates global h- and p-refinements with a coarsening step. Thus, at each unrefinement step, we eliminate the basis functions with the lowest contributions to the solution. When solving elliptic problems using energy-norm adaptivity, the removed basis functions are those with the lowest contributions to the energy of the solution. For non-elliptic problems or goal-oriented adaptivity, we propose an upper bound of the error representation expressed in terms of an inner product of the specific equation, leading to error indicators that deliver quasi-optimal hp-unrefinements. This unrefinement strategy removes unneeded unknowns possibly introduced during the pre-asymptotical regime. In addition, the grids over which we perform the unrefinements are arbitrary, and thus, we can limit their size and associated computational costs. We numerically analyze our algorithm for energy-norm and goal-oriented adaptivity. In particular, we solve two-dimensional (2D) Poisson, Helmholtz, convection-dominated equations, and a three-dimensional (3D) Helmholtz-like problem. In all cases, we observe exponential convergence rates. Our algorithm is robust and straightforward to implement; therefore, it can be easily adapted for industrial applications.Elsevier202620262022info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/77539reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoIngléshttps://doi.org/10.1016/j.cma.2022.115641info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/3.0/es/© 2022 The Authors. Published by Elsevier B.V. under the Creative Commons CC-BY-NC-ND licenseoai:addi.ehu.eus:10810/775392026-06-18T09:23:17Z
dc.title.none.fl_str_mv A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
title A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
spellingShingle A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
Caro Gutiérrez, Felipe Vinicio
goal-oriented adaptivity
hp-adaptivity
finite element method
unrefinements
non-elliptic problems
title_short A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
title_full A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
title_fullStr A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
title_full_unstemmed A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
title_sort A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
dc.creator.none.fl_str_mv Caro Gutiérrez, Felipe Vinicio
Darrigrand, Vincent
Alvarez Aramberri, Julen
Alberdi Celaya, Elisabete
Pardo Zubiaur, David
author Caro Gutiérrez, Felipe Vinicio
author_facet Caro Gutiérrez, Felipe Vinicio
Darrigrand, Vincent
Alvarez Aramberri, Julen
Alberdi Celaya, Elisabete
Pardo Zubiaur, David
author_role author
author2 Darrigrand, Vincent
Alvarez Aramberri, Julen
Alberdi Celaya, Elisabete
Pardo Zubiaur, David
author2_role author
author
author
author
dc.subject.none.fl_str_mv goal-oriented adaptivity
hp-adaptivity
finite element method
unrefinements
non-elliptic problems
topic goal-oriented adaptivity
hp-adaptivity
finite element method
unrefinements
non-elliptic problems
description This work extends an automatic energy-norm hp-adaptive strategy based on performing quasi-optimal unrefinements to the case of non-elliptic problems and goal-oriented adaptivity. The proposed approach employs a multi-level hierarchical data structure and alternates global h- and p-refinements with a coarsening step. Thus, at each unrefinement step, we eliminate the basis functions with the lowest contributions to the solution. When solving elliptic problems using energy-norm adaptivity, the removed basis functions are those with the lowest contributions to the energy of the solution. For non-elliptic problems or goal-oriented adaptivity, we propose an upper bound of the error representation expressed in terms of an inner product of the specific equation, leading to error indicators that deliver quasi-optimal hp-unrefinements. This unrefinement strategy removes unneeded unknowns possibly introduced during the pre-asymptotical regime. In addition, the grids over which we perform the unrefinements are arbitrary, and thus, we can limit their size and associated computational costs. We numerically analyze our algorithm for energy-norm and goal-oriented adaptivity. In particular, we solve two-dimensional (2D) Poisson, Helmholtz, convection-dominated equations, and a three-dimensional (3D) Helmholtz-like problem. In all cases, we observe exponential convergence rates. Our algorithm is robust and straightforward to implement; therefore, it can be easily adapted for industrial applications.
publishDate 2022
dc.date.none.fl_str_mv 2022
2026
2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/77539
url http://hdl.handle.net/10810/77539
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1016/j.cma.2022.115641
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
© 2022 The Authors. Published by Elsevier B.V. under the Creative Commons CC-BY-NC-ND license
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/3.0/es/
© 2022 The Authors. Published by Elsevier B.V. under the Creative Commons CC-BY-NC-ND license
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:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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