A two-grid method for discontinuous Galerkin approximations to compressible miscible displacement problems. (1st June 2022) - Yang, Jiming; Zhou, Jing; Nie, Cunyun
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 H 1 error estimate of the concentration and the L 2 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 ( H 2 ) . The numerical results are presented to confirm that the algorithm is effective.