# Finite element discretization of Darcy's equations with pressure dependent porosity

Vivette Girault; François Murat; Abner Salgado

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 6, page 1155-1191
- ISSN: 0764-583X

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topGirault, Vivette, Murat, François, and Salgado, Abner. "Finite element discretization of Darcy's equations with pressure dependent porosity." ESAIM: Mathematical Modelling and Numerical Analysis 44.6 (2010): 1155-1191. <http://eudml.org/doc/250842>.

@article{Girault2010,

abstract = {
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.
},

author = {Girault, Vivette, Murat, François, Salgado, Abner},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Porous media flows; Darcy equations; finite elements; exponential porosity; bounded porosity; convergence; splitting scheme},

language = {eng},

month = {10},

number = {6},

pages = {1155-1191},

publisher = {EDP Sciences},

title = {Finite element discretization of Darcy's equations with pressure dependent porosity},

url = {http://eudml.org/doc/250842},

volume = {44},

year = {2010},

}

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

DA - 2010/10//

PB - EDP Sciences

VL - 44

IS - 6

SP - 1155

EP - 1191

AB -
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.

LA - eng

KW - Porous media flows; Darcy equations; finite elements; exponential porosity; bounded porosity; convergence; splitting scheme

UR - http://eudml.org/doc/250842

ER -

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