Two-grid method for compressible miscible displacement problem by CFEM-MFEM

This paper is concerned about the error analysis of two-grid method for compressible miscible displacement in porous medium. A characteristics finite element method (CFEM) is presented for the concentration equation to handle the convection part, and standard mixed finite element method (MFEM) is used for the pressure equation. Moreover, we linearize the equations based on the Newton iteration method, then, two-grid method is considered in this full discrete scheme problem. We prove the Lp error estimates for the pressure, Darcy velocity, concentration variables in the two-grid method. It is shown that coarse space can be extremely coarse and we achieve asymptotically optimal approximation. Finally, numerical experiment indicates that two-grid method is a very effective method for solving miscible displacement problem.