Abstract
This is the fifth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we study a finite element procedure for numerically solving this system. This procedure uses a mixed finite element method for the elliptic equation of the pressure and velocity and the modified method of characteristics for the degenerate parabolic equation of the saturation. Sharp error estimates in energy norms are obtained for this procedure. The error analysis does not use any regularization of the saturation equation and does not impose any restriction on the nature of degeneracy; these error estimates are derived directly from this degenerate saturation equation. Other characteristic finite element methods such as the modified method of characteristics with adjusted advection (MMOCAA) are also considered.
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