A combined discontinuous Galerkin finite element method for miscible displacement problem

A new combined method is constructed for solving incompressible miscible displacement in porous media. In this procedure, a hybrid mixed element method is constructed for the pressure and velocity equation, while a symmetric discontinuous Galerkin finite element method is proposed for the concentration equation. The introduction of these two numerical methods not only makes the coefficient matrixes symmetric positive definite, but also conserves the local mass balance. The stability and consistency of the method are analyzed and the optimal error estimate in L∞(L2)L∞(L2) for velocity and concentration and the super convergence in L∞(H1)L∞(H1) for pressure are derived. Finally, some numerical results are presented.