A Two-Grid Combined Mixed Finite Element and Discontinuous Galerkin Method for an Incompressible Miscible Displacement Problem in Porous Media

摘要

An incompressible miscible displacement problem is investigated. A two-grid algorithm of a full-discretized combined mixed finite element and discontinuous Galerkin approximation to the miscible displacement in porous media is proposed. The error estimate for the concentration in H1-norm and the error estimates for the pressure and the velocity in L2-norm are obtained. The analysis shows that the asymptotically optimal approximation can be achieved as long as the mesh size satisfies h=O(H2), where H and h are the sizes of the coarse mesh and the fine mesh, respectively. Meanwhile, the effectiveness of the presented algorithm is verified by numerical experiments, from which it can be seen that the algorithm is spent much less time.