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

Vivette Girault, François Murat, Abner Salgado

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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. © 2010 EDP Sciences, SMAI.
Original languageEnglish (US)
Pages (from-to)1155-1191
Number of pages37
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume44
Issue number6
DOIs
StatePublished - Feb 23 2010
Externally publishedYes

Fingerprint Dive into the research topics of 'Finite element discretization of Darcy's equations with pressure dependent porosity'. Together they form a unique fingerprint.

Cite this