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Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients

Published online by Cambridge University Press:  04 October 2007

Zakaria Belhachmi ,
Christine Bernardi  and
Andreas Karageorghis
Zakaria Belhachmi
Affiliation:
L.M.A.M. (UMR 7122), Université Paul Verlaine-Metz, Ile de Saulcy, 57045 Metz Cedex 01, France.
Christine Bernardi
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. [email protected]
Andreas Karageorghis
Affiliation:
Dept. of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus.
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Abstract

This paper deals with the mortar spectral element discretization of two equivalent problems, the Laplace equation and the Darcy system, in a domain which corresponds to a nonhomogeneous anisotropic medium. The numerical analysis of the discretization leads to optimal error estimates and the numerical experiments that we present enable us to verify its efficiency.

Keywords

Mortar methodspectral elementsLaplace equationDarcy equation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 4 , July 2007 , pp. 801 - 824
Copyright
© EDP Sciences, SMAI, 2007

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