Coupling Darcy and Stokes equations for porous media with cracks
Laboratoire Jacques-Louis Lions, CNRS & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France.
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Revised: 2 March 2003
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.
Mathematics Subject Classification: 65N30 / 65N50 / 76D07 / 76S05
Key words: Darcy and Stokes equations / finite elements / error estimates.
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