Finite element method for two-phase immiscible flow

An explicit finite element method for numerically solving the two-phase, im miscible, incompressible flow in a porous medium in two space dimensions is analyzed. The method is based on the use of a mixed finite element method for the approximation of the velocity and pressure a discontinuous upwindin g finite element method for the approximation of the saturation. The mixed method gives an approximate velocity field in the precise form needed by th e discontinuous method, which is trivially conservative and fully paralleli zable in computation. It is proven that it converges to the exact solution. (C) 1999 John Wiley & Sons, Inc.