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.
@article{M2AN_2005__39_1_7_0,
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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {39},
year = {2005},
pages = {7-35},
doi = {10.1051/m2an:2005007},
mrnumber = {2136198},
zbl = {1079.76041},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2005__39_1_7_0}
}
Bernardi, Christine; Hecht, Frédéric; Pironneau, Olivier. Coupling Darcy and Stokes equations for porous media with cracks. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 7-35. doi : 10.1051/m2an:2005007. http://gdmltest.u-ga.fr/item/M2AN_2005__39_1_7_0/
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