Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems
- Autores
- Cheddadi, I.; Fučík, R.; Prieto, M.I.; Vohralík, M.
- Año de publicación
- 2009
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order Raviart-Thomas-Nédélec space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincaré, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates. © 2009 EDP Sciences SMAI.
Fil:Prieto, M.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. - Fuente
- Math. Model. Numer. Anal. 2009;43(5):867-888
- Materia
-
A posteriori error estimates
Guaranteed upper bound
Robustness
Singularly perturbed reaction-diffusion problem
Vertex-centered finite volume/finite volume element/box method - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/2.5/ar
- Repositorio
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_0764583X_v43_n5_p867_Cheddadi
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Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problemsCheddadi, I.Fučík, R.Prieto, M.I.Vohralík, M.A posteriori error estimatesGuaranteed upper boundRobustnessSingularly perturbed reaction-diffusion problemVertex-centered finite volume/finite volume element/box methodWe derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order Raviart-Thomas-Nédélec space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincaré, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates. © 2009 EDP Sciences SMAI.Fil:Prieto, M.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0764583X_v43_n5_p867_CheddadiMath. Model. Numer. Anal. 2009;43(5):867-888reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:42:55Zpaperaa:paper_0764583X_v43_n5_p867_CheddadiInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:42:56.496Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
dc.title.none.fl_str_mv |
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems |
title |
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems |
spellingShingle |
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems Cheddadi, I. A posteriori error estimates Guaranteed upper bound Robustness Singularly perturbed reaction-diffusion problem Vertex-centered finite volume/finite volume element/box method |
title_short |
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems |
title_full |
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems |
title_fullStr |
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems |
title_full_unstemmed |
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems |
title_sort |
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems |
dc.creator.none.fl_str_mv |
Cheddadi, I. Fučík, R. Prieto, M.I. Vohralík, M. |
author |
Cheddadi, I. |
author_facet |
Cheddadi, I. Fučík, R. Prieto, M.I. Vohralík, M. |
author_role |
author |
author2 |
Fučík, R. Prieto, M.I. Vohralík, M. |
author2_role |
author author author |
dc.subject.none.fl_str_mv |
A posteriori error estimates Guaranteed upper bound Robustness Singularly perturbed reaction-diffusion problem Vertex-centered finite volume/finite volume element/box method |
topic |
A posteriori error estimates Guaranteed upper bound Robustness Singularly perturbed reaction-diffusion problem Vertex-centered finite volume/finite volume element/box method |
dc.description.none.fl_txt_mv |
We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order Raviart-Thomas-Nédélec space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincaré, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates. © 2009 EDP Sciences SMAI. Fil:Prieto, M.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. |
description |
We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order Raviart-Thomas-Nédélec space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincaré, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates. © 2009 EDP Sciences SMAI. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009 |
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/20.500.12110/paper_0764583X_v43_n5_p867_Cheddadi |
url |
http://hdl.handle.net/20.500.12110/paper_0764583X_v43_n5_p867_Cheddadi |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by/2.5/ar |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
Math. Model. Numer. Anal. 2009;43(5):867-888 reponame:Biblioteca Digital (UBA-FCEN) instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales instacron:UBA-FCEN |
reponame_str |
Biblioteca Digital (UBA-FCEN) |
collection |
Biblioteca Digital (UBA-FCEN) |
instname_str |
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
instacron_str |
UBA-FCEN |
institution |
UBA-FCEN |
repository.name.fl_str_mv |
Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
repository.mail.fl_str_mv |
ana@bl.fcen.uba.ar |
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