Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces

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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...

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Autores principales:	Durán, R.G., Lombardi, A.L.
Formato:	JOUR
Materias:	Anisotropic elements Weighted norms
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00255718_v74_n252_p1679_Duran
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00255718_v74_n252_p1679_Duran
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spelling	todo:paper_00255718_v74_n252_p1679_Duran2023-10-03T14:36:11Z Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces Durán, R.G. Lombardi, A.L. Anisotropic elements Weighted norms 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00255718_v74_n252_p1679_Duran
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Anisotropic elements Weighted norms
spellingShingle	Anisotropic elements Weighted norms Durán, R.G. Lombardi, A.L. Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces
topic_facet	Anisotropic elements Weighted norms
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.
format	JOUR
author	Durán, R.G. Lombardi, A.L.
author_facet	Durán, R.G. Lombardi, A.L.
author_sort	Durán, R.G.
title	Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces
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
url	http://hdl.handle.net/20.500.12110/paper_00255718_v74_n252_p1679_Duran
work_keys_str_mv	AT duranrg errorestimatesonanisotropicq1elementsforfunctionsinweightedsobolevspaces AT lombardial errorestimatesonanisotropicq1elementsforfunctionsinweightedsobolevspaces
_version_	1807320250273759232

Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces

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