A finite element method for degenerate two-phase flow in porous media. I. Well-posedness (Q1983653)

In this work, a finite element method to solve the immiscible two-phase flow problem in porous media, is formulated. It is known that the preferred unknowns in industrial reservoir simulators are the phase pressure and saturation. The proposed method approximates these unknowns, directly. The discrete saturation satisfies a maximum principle. The numerical method employs mass lumping for integration and an upwind flux technique. Existence of the numerical solutions and some stability bounds are proved. It is also shown that the numerical saturation is bounded between zero and one.