A two-grid method for discontinuous Galerkin approximations to compressible miscible displacement problems

Abstract

Discontinuous Galerkin approximations are employed to the compressible miscible displacement problem. A two-grid algorithm is proposed, which is based on one coarse grid space and one fine grid space. The H1 error estimate of the concentration and the L2 error estimate of the velocity are presented for the proposed two-grid method, which show that the two-grid method achieves optimal approximations if the mesh sizes satisfy h=O(H2). The numerical results are presented to confirm that the algorithm is effective.