A new MMOCAA-MFE method for compressible miscible displacement in porous media

Combining the modified method of characteristics with adjusted advection with a splitting positive definite mixed element scheme, we establish a new mixed finite element procedure for solving compressible miscible displacement in porous media. This procedure can preserve the mass conservation globally, the coefficient matrix of the mixed system is symmetric positive definite and the flux equation is separated from the pressure equation. We analyse the convergence and give an optimal L2L2-norm error estimate. Finally we present some numerical results to confirm our theoretical analysis.