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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Detalles Bibliográficos
Autores principales:	Acosta Rodriguez, Gabriel, Duran, Ricardo Guillermo
Publicado:	2000
Materias:	Maximum angle Mixed Nonconforming Raviart-Thomas Stokes
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v37_n1_p18_Acosta 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	paper:paper_00361429_v37_n1_p18_Acosta
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spelling	paper:paper_00361429_v37_n1_p18_Acosta2023-06-08T15:01:57Z The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo 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. 2000 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v37_n1_p18_Acosta 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 Rodriguez, Gabriel Duran, Ricardo Guillermo 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.
author	Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo
author_facet	Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo
author_sort	Acosta Rodriguez, Gabriel
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
publishDate	2000
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v37_n1_p18_Acosta http://hdl.handle.net/20.500.12110/paper_00361429_v37_n1_p18_Acosta
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The maximum angle condition for mixed and nonconforming elements: Application to the stokes equations

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