Mixed finite element-finite volume methods

Abstract

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.