Geodesic
Coupling Darcy and Stokes equations for porous media with cracks
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 1, pp. 7-35

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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.

DOI : 10.1051/m2an:2005007
Classification : 65N30, 65N50, 76D07, 76S05
Keywords: Darcy and Stokes equations, finite elements, error estimates 
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     author = {Bernardi, Christine and Hecht, Fr\'ed\'eric and Pironneau, Olivier},
     title = {Coupling {Darcy} and {Stokes} equations for porous media with cracks},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {7--35},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {1},
     year = {2005},
     doi = {10.1051/m2an:2005007},
     mrnumber = {2136198},
     zbl = {1079.76041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005007/}
}
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Bernardi, Christine; Hecht, Frédéric; Pironneau, Olivier. Coupling Darcy and Stokes equations for porous media with cracks. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 1, pp. 7-35. doi: 10.1051/m2an:2005007

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