Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces
- Autores
- Durán, R.G.; Lombardi, A.L.
- Año de publicación
- 2005
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained. © 2005 American Mathematical Society.
Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. - Fuente
- Math. Comput. 2005;74(252):1679-1706
- Materia
-
Anisotropic elements
Weighted norms - 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_00255718_v74_n252_p1679_Duran
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Error estimates on anisotropic Q1 elements for functions in weighted sobolev spacesDurán, R.G.Lombardi, A.L.Anisotropic elementsWeighted normsIn this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained. © 2005 American Mathematical Society.Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2005info: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_00255718_v74_n252_p1679_DuranMath. Comput. 2005;74(252):1679-1706reponame: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/ar2025-09-29T13:43:06Zpaperaa:paper_00255718_v74_n252_p1679_DuranInstitucionalhttps://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 13:43:07.546Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
dc.title.none.fl_str_mv |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
title |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
spellingShingle |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces Durán, R.G. Anisotropic elements Weighted norms |
title_short |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
title_full |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
title_fullStr |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
title_full_unstemmed |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
title_sort |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
dc.creator.none.fl_str_mv |
Durán, R.G. Lombardi, A.L. |
author |
Durán, R.G. |
author_facet |
Durán, R.G. Lombardi, A.L. |
author_role |
author |
author2 |
Lombardi, A.L. |
author2_role |
author |
dc.subject.none.fl_str_mv |
Anisotropic elements Weighted norms |
topic |
Anisotropic elements Weighted norms |
dc.description.none.fl_txt_mv |
In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained. © 2005 American Mathematical Society. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. |
description |
In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained. © 2005 American Mathematical Society. |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005 |
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_00255718_v74_n252_p1679_Duran |
url |
http://hdl.handle.net/20.500.12110/paper_00255718_v74_n252_p1679_Duran |
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. Comput. 2005;74(252):1679-1706 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) |
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Biblioteca Digital (UBA-FCEN) |
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Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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UBA-FCEN |
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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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