A new MCC–MFE method for compressible miscible displacement in porous media

This paper presents a new mass-conservative finite element method for solving the compressible miscible displacement problem in porous media. This new method combines characteristic tracking with the mixed finite element method. Specifically, the mass-conservative characteristic finite element method is applied to the concentration equation whereas the mixed finite element method with continuous flux approximation is used for the flow equation. This procedure conserves mass globally. Convergence of the fully discrete scheme is analyzed and optimal L2L2-norm and H1H1-norm error estimates for the concentration are obtained. Numerical experiments are presented to illustrate the theoretical analysis.