  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.
