A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem

A compressible miscible displacement problem is modeled by a nonlinear coupled system with partial differential equations in porous media. A two-grid algorithm of a combined mixed finite element and discontinuous Galerkin approximation is proposed based on the Newton iteration method. The error estimate in H-1-norm for concentration and the error estimate in L-2-norm for velocity are derived. It is shown that an asymptotically optimal approximation rate with the two-grid algorithm can be achieved if h = O(H-2) is satisfied, where H and h are mesh sizes of the coarse grid and the fine grid, respectively. Numerical experiments indicate that the two-grid algorithm is effective, which coincides the theoretical analysis.