2020/01/24 by Vivette, Girault, Beatrice, Riviere, Loic, Cappanera
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2001.08859
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.