A finite element method for degenerate two-phase flow in porous media. Part II: Convergence

Abstract Convergence of a finite element method with mass-lumping and flux upwinding is formulated for solving the immiscible two-phase flow problem in porous media. The approximates directly wetting phase pressure saturation, which are primary unknowns. Well-posedness obtained [J. Numer. Math., 29(2), 2021]. Theoretical convergence proved via compactness argument. numerical saturation converges strongly to weak solution L 2 space time whereas pressures converge solutions almost everywhere time. proof not straightforward because degeneracy mobilities unboundedness derivative capillary pressure.