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.
Mots clés : Darcy and Stokes equations, finite elements, error estimates
@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: Mod\'elisation math\'ematique et analyse num\'erique}, 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://www.numdam.org/articles/10.1051/m2an:2005007/} }
TY - JOUR AU - Bernardi, Christine AU - Hecht, Frédéric AU - Pironneau, Olivier TI - Coupling Darcy and Stokes equations for porous media with cracks JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 7 EP - 35 VL - 39 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005007/ DO - 10.1051/m2an:2005007 LA - en ID - M2AN_2005__39_1_7_0 ER -
%0 Journal Article %A Bernardi, Christine %A Hecht, Frédéric %A Pironneau, Olivier %T Coupling Darcy and Stokes equations for porous media with cracks %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 7-35 %V 39 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005007/ %R 10.1051/m2an:2005007 %G en %F M2AN_2005__39_1_7_0
Bernardi, Christine; Hecht, Frédéric; Pironneau, Olivier. Coupling Darcy and Stokes equations for porous media with cracks. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 1, pp. 7-35. doi : 10.1051/m2an:2005007. http://www.numdam.org/articles/10.1051/m2an:2005007/
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