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Mortar finite element discretization of a model coupling Darcy and Stokes equations

Published online by Cambridge University Press:  03 April 2008

Christine Bernardi ,
Tomás Chacón Rebollo ,
Frédéric Hecht  and
Zoubida Mghazli
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. bernardi@ann.jussieu.fr; hecht@ann.jussieu.fr
Tomás Chacón Rebollo
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. bernardi@ann.jussieu.fr; hecht@ann.jussieu.fr Departamento de Ecuaciones Diferenciales y Análisis Numerico, Universidad de Sevilla, Tarfia s/n, 41012 Sevilla, Spain. chacon@numer.us.es
Frédéric Hecht
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. bernardi@ann.jussieu.fr; hecht@ann.jussieu.fr
Zoubida Mghazli
Affiliation:
Équipe d'Ingénierie Mathématique, LIRNE, Faculté des Sciences, Université Ibn Tofail, B.P. 133, Kénitra, Morocco. mghazli_zoubida@yahoo.com
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Abstract

As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove a priori and a posteriori error estimates for the resulting discrete problem. Some numerical experiments confirm the interest of the discretization.

Keywords

Mortar methodfinite elementsDarcy equationsStokes equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 3 , May 2008 , pp. 375 - 410
Copyright
© EDP Sciences, SMAI, 2008

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