(untitled) (Journal of Computational Mathematics, 2022)
A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The concentration equation is treated by a mixed finite element method with characteristics (CMFEM) and the pressure equation is treated by a parabolic mixed finite element method (PMFEM). Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations. Moreover, the L^q error estimates are conducted for the pressure, Darcy velocity and concentration variables in the two-grid solutions. Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.