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Some mixed finite element methodson anisotropic meshes

Published online by Cambridge University Press:  15 April 2002

Mohamed Farhloul ,
Serge Nicaise  and
Luc Paquet
Mohamed Farhloul
Affiliation:
Université de Moncton, Département de Mathématiques et de Statistique, N.B., E1A 3 E9, Moncton, Canada. (farhlom@umoncton.ca)
Serge Nicaise
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, ISTV, 59313 Valenciennes Cedex 9, France. (snicaise@univ-valenciennes.fr),
Luc Paquet
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, ISTV, 59313 Valenciennes Cedex 9, France. (Luc.Paquet@univ-valenciennes.fr)
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Abstract

The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic regularity results of the solutions.

Keywords

Anisotropic meshRaviart-Thomas elementanisotropic interpolation error estimateLaplace equationedge singularitymixed FEM.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 5 , September 2001 , pp. 907 - 920
Copyright
© EDP Sciences, SMAI, 2001

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