A posteriori error estimates of mixed methods for miscible displacement problems

The miscible displacement of one incompressible fluid by another in a porous medium is governed by a system of two equations.One is an elliptic equation of the pressure and the other is a parabolic equation of the concentration of one of the fluids.Since the pressure appears in the concentration only through its velocity field,we choose a mixed finite element method to approximate the pressure equation and for the concentration we use the standard Galerkin method.We shall obtain an explicit a posteriori error estimator in L-2(L-2) for the serni-discrete scheme applied to the non-linear coupled system.