Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra

We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three-dimensional maximum angle condition and the regular vertex property, for tetrahe...

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Autores principales:	Acosta, G., Apel, T., Durán, R.G., Lombardi, A.L.
Formato:	JOUR
Materias:	Anisotropic finite elements Mixed finite elements Raviart-thomas
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00255718_v80_n273_p141_Acosta
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00255718_v80_n273_p141_Acosta
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spelling	todo:paper_00255718_v80_n273_p141_Acosta2023-10-03T14:36:13Z Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra Acosta, G. Apel, T. Durán, R.G. Lombardi, A.L. Anisotropic finite elements Mixed finite elements Raviart-thomas We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three-dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject, and the results obtained are more general in several aspects. First, intermediate regularity is allowed; that is, for the Raviart-Thomas interpolation of degree k ≥ 0, we prove error estimates of order j + 1 when the vector field being approximated has components in WJ+1,p, for triangles or tetrahedra, where 0 ≤ j ≤ k and 1 ≤ p ≤ ∞. These results are new even in the two-dimensional case. Indeed, the estimate was known only in the case j = k. On the other hand, in the three-dimensional case, results under the maximum angle condition were known only for k = 0. © 2010 American Mathematical Society. Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 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_v80_n273_p141_Acosta
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 finite elements Mixed finite elements Raviart-thomas
spellingShingle	Anisotropic finite elements Mixed finite elements Raviart-thomas Acosta, G. Apel, T. Durán, R.G. Lombardi, A.L. Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra
topic_facet	Anisotropic finite elements Mixed finite elements Raviart-thomas
description	We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three-dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject, and the results obtained are more general in several aspects. First, intermediate regularity is allowed; that is, for the Raviart-Thomas interpolation of degree k ≥ 0, we prove error estimates of order j + 1 when the vector field being approximated has components in WJ+1,p, for triangles or tetrahedra, where 0 ≤ j ≤ k and 1 ≤ p ≤ ∞. These results are new even in the two-dimensional case. Indeed, the estimate was known only in the case j = k. On the other hand, in the three-dimensional case, results under the maximum angle condition were known only for k = 0. © 2010 American Mathematical Society.
format	JOUR
author	Acosta, G. Apel, T. Durán, R.G. Lombardi, A.L.
author_facet	Acosta, G. Apel, T. Durán, R.G. Lombardi, A.L.
author_sort	Acosta, G.
title	Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra
title_short	Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra
title_full	Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra
title_fullStr	Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra
title_full_unstemmed	Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra
title_sort	error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra
url	http://hdl.handle.net/20.500.12110/paper_00255718_v80_n273_p141_Acosta
work_keys_str_mv	AT acostag errorestimatesforraviartthomasinterpolationofanyorderonanisotropictetrahedra AT apelt errorestimatesforraviartthomasinterpolationofanyorderonanisotropictetrahedra AT duranrg errorestimatesforraviartthomasinterpolationofanyorderonanisotropictetrahedra AT lombardial errorestimatesforraviartthomasinterpolationofanyorderonanisotropictetrahedra
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Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra

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