This paper is devoted to present a numerical methods for a model
of incompressible and miscible flow
in porous media. We analyze a numerical
scheme combining a mixed finite element method (MFE) and finite
volume scheme (FV) for solving a coupled system includes an
elliptic equation
(pressure and velocity) and a linear convection-diffusion equation
(concentration). The (FV) scheme considered is "vertex centered" type
semi implicit. We show that this scheme is $L^{\infty}$, BV stable
under a CFL condition and satisfies a discrete maximum principle.
We prove also the convergence of the approximate solution obtained
by the combined scheme (MFE)-(FV) to the solution of the coupled
system. Finally the numerical results are presented for two spaces
dimensions problem
in a homogenous isotropic
medium.