APPROXIMATION OF A DIFFUSION-CONVECTION EQUATION BY A MIXED FINITE-ELEMENT METHOD - APPLICATION TO THE WATER FLOODING PROBLEM

Diphasic incompressible flows in porous media are modeled by a system of two nonlinear equations, namely a diffusion convection equation and an elliptic one. The diffusion term of the first equation may vanish so that the convective term dominates and the solution has stiff fronts. The diffusion term is approximated by a mixed finite element method associated, for the convective term, with an ″upwind″ scheme for discontinuous elements. A complete error analysis being out of reach, the author restricts himself to the linear stationary case, and concludes by presenting numerical experiments concerning the resolution of the water-flooding problem. The physical motivation of this work is the recovering of oil from a reservoir by injection of water.