CONVERGENCE OF A FINITE ELEMENT METHOD FOR DEGENERATE TWO-PHASE FLOW IN POROUS MEDIA

Vivette Girault (1) , Béatrice Rivière (2) , Loïc Cappanera (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Department of Computational and Applied Mathematics, Rice University
3 Department of Mathematics, University of Houston

A finite element method with mass-lumping and flux upwinding, is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the wetting phase pressure and saturation, which are the primary unknowns. The discrete saturation satisfies a maximum principle. Theoretical convergence is proved via a compactness argument. The proof is convoluted because of the degeneracy of the phase mobilities and the unboundedness of the capillary pressure.

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Vivette Girault, Béatrice Rivière, Loïc Cappanera. CONVERGENCE OF A FINITE ELEMENT METHOD FOR DEGENERATE TWO-PHASE FLOW IN POROUS MEDIA. 2020. ⟨hal-02453608⟩