Finite element discretization of Darcy's equations with pressure dependent porosity
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) no. 6, p. 1155-1191
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.
@article{M2AN_2010__44_6_1155_0,
     author = {Girault, Vivette and Murat, Fran\c cois and Salgado, Abner},
     title = {Finite element discretization of Darcy's equations with pressure dependent porosity},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {6},
     year = {2010},
     pages = {1155-1191},
     doi = {10.1051/m2an/2010019},
     zbl = {pre05835017},
     mrnumber = {2769053},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) no. 6, pp. 1155-1191. doi : 10.1051/m2an/2010019. http://www.numdam.org/item/M2AN_2010__44_6_1155_0/

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