A mixed element method for Darcy-Forchheimer incompressible miscible displacement problem

A numerical scheme for incompressible miscible displacement problem in porous media is considered in which the velocity-pressure relation is described by the Darcy-Forchheimer equation. Mixed element such as Raviart-Thomas element, Brezzi-Douglas-Marini element is used to handle the Darcy-Forchheimer equation and standard finite element is used to approximate concentration. Error estimates for velocity, pressure and concentration in different norms are established. Numerical experiments are given to verify the efficiency of the presented scheme.