We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods.
Mots clés : porous media flows, Darcy equations, finite elements
@article{M2AN_2010__44_6_1155_0,
author = {Girault, Vivette and Murat, Fran\c{c}ois and Salgado, Abner},
title = {Finite element discretization of {Darcy's} equations with pressure dependent porosity},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1155--1191},
publisher = {EDP-Sciences},
volume = {44},
number = {6},
year = {2010},
doi = {10.1051/m2an/2010019},
mrnumber = {2769053},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2010019/}
}
TY - JOUR AU - Girault, Vivette AU - Murat, François AU - Salgado, Abner TI - Finite element discretization of Darcy's equations with pressure dependent porosity JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2010 SP - 1155 EP - 1191 VL - 44 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2010019/ DO - 10.1051/m2an/2010019 LA - en ID - M2AN_2010__44_6_1155_0 ER -
%0 Journal Article %A Girault, Vivette %A Murat, François %A Salgado, Abner %T Finite element discretization of Darcy's equations with pressure dependent porosity %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2010 %P 1155-1191 %V 44 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2010019/ %R 10.1051/m2an/2010019 %G en %F M2AN_2010__44_6_1155_0
Girault, Vivette; Murat, François; Salgado, Abner. Finite element discretization of Darcy's equations with pressure dependent porosity. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 6, pp. 1155-1191. doi : 10.1051/m2an/2010019. http://archive.numdam.org/articles/10.1051/m2an/2010019/
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