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Coupling Darcy and Stokes equations for porous media with cracks

Published online by Cambridge University Press:  15 March 2005

Christine Bernardi ,
Frédéric Hecht  and
Olivier Pironneau
Christine Bernardi
Affiliation:
Laboratoire Jacques-Louis Lions, CNRS & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr; hecht@ann.jussieu.fr; pironneau@ann.jussieu.fr
Frédéric Hecht
Affiliation:
Laboratoire Jacques-Louis Lions, CNRS & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr; hecht@ann.jussieu.fr; pironneau@ann.jussieu.fr
Olivier Pironneau
Affiliation:
Laboratoire Jacques-Louis Lions, CNRS & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr; hecht@ann.jussieu.fr; pironneau@ann.jussieu.fr
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Abstract

In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive a priori and a posteriori error estimates. We present some numerical experiments that are in good agreement with the analysis.

Keywords

Darcy and Stokes equationsfinite elementserror estimates.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 1 , January 2005 , pp. 7 - 35
Copyright
© EDP Sciences, SMAI, 2005

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