A finite element method for degenerate two-phase flow in porous media. Part I: Well-posedness

Vivette Girault (1) , Beatrice Riviere (2) , Loic Cappanera (3)

1 LJLL (UMR_7598) - 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. Stability of the scheme and existence of a solution are established.

Mots clés: stability compactness maximum principle pressure-saturation Classification: 65M60 65M12; stability; compactness; maximum principle; pressure-saturation Classification: 65M60; 65M12

Domaines: Mathématiques [math]

Vivette Girault, Beatrice Riviere, Loic Cappanera. A finite element method for degenerate two-phase flow in porous media. Part I: Well-posedness. Journal of Numerical Mathematics, 2021, ⟨10.1515/jnma-2020-0004⟩. ⟨hal-03876351⟩