The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations

For the Lagrange interpolation it is known that optimal order error estimates hold for elements satisfying the maximum angle condition. The objective of this paper is to obtain similar results for the Raviart-Thomas interpolation arising in the analysis of mixed methods. We prove that optimal order...

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Autores principales: Acosta, G., Durán, R.G.
Formato: JOUR
Materias:
Maximum angle
Mixed
Nonconforming
Raviart-Thomas
Stokes
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00361429_v37_n1_p18_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00361429_v37_n1_p18_Acosta
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spelling todo:paper_00361429_v37_n1_p18_Acosta2023-10-03T14:47:42Z The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations Acosta, G. Durán, R.G. Maximum angle Mixed Nonconforming Raviart-Thomas Stokes For the Lagrange interpolation it is known that optimal order error estimates hold for elements satisfying the maximum angle condition. The objective of this paper is to obtain similar results for the Raviart-Thomas interpolation arising in the analysis of mixed methods. We prove that optimal order error estimates hold under the maximum angle condition for this interpolation both in two and three dimensions and, moreover, that this condition is indeed necessary to have these estimates. Error estimates for the mixed approximation of second order elliptic problems and for the nonconforming piecewise linear approximation of the Stokes equations are derived from our results. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00361429_v37_n1_p18_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 Maximum angle
Mixed
Nonconforming
Raviart-Thomas
Stokes
spellingShingle Maximum angle
Mixed
Nonconforming
Raviart-Thomas
Stokes
Acosta, G.
Durán, R.G.
The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations
topic_facet Maximum angle
Mixed
Nonconforming
Raviart-Thomas
Stokes
description For the Lagrange interpolation it is known that optimal order error estimates hold for elements satisfying the maximum angle condition. The objective of this paper is to obtain similar results for the Raviart-Thomas interpolation arising in the analysis of mixed methods. We prove that optimal order error estimates hold under the maximum angle condition for this interpolation both in two and three dimensions and, moreover, that this condition is indeed necessary to have these estimates. Error estimates for the mixed approximation of second order elliptic problems and for the nonconforming piecewise linear approximation of the Stokes equations are derived from our results.
format JOUR
author Acosta, G.
Durán, R.G.
author_facet Acosta, G.
Durán, R.G.
author_sort Acosta, G.
title The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations
title_short The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations
title_full The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations
title_fullStr The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations
title_full_unstemmed The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations
title_sort maximum angle condition for mixed and nonconforming elements: application to the stokes equations
url http://hdl.handle.net/20.500.12110/paper_00361429_v37_n1_p18_Acosta
work_keys_str_mv AT acostag themaximumangleconditionformixedandnonconformingelementsapplicationtothestokesequations
AT duranrg themaximumangleconditionformixedandnonconformingelementsapplicationtothestokesequations
AT acostag maximumangleconditionformixedandnonconformingelementsapplicationtothestokesequations
AT duranrg maximumangleconditionformixedandnonconformingelementsapplicationtothestokesequations
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