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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. ([email protected])
Serge Nicaise
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, ISTV, 59313 Valenciennes Cedex 9, France. ([email protected]),
Luc Paquet
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, ISTV, 59313 Valenciennes Cedex 9, France. ([email protected])
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Abstract

The paper deals with some mixed finite element methods on a classof anisotropic meshes based on tetrahedra and prismatic (pentahedral)elements. Anisotropic localinterpolation error estimates are derived in some anisotropic weighted Sobolevspaces. As particularapplications, the numerical approximation by mixed methods of the Laplace equationin domainswith edges is investigated where anisotropic finiteelement meshes are appropriate. Optimal error estimates are obtained using some anisotropic regularity results of thesolutions.

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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