| Abstract: | Finite element methods are used to solve a coupled system of nonlinear partial differential equations, which models incompressible miscible displacement in porous media. Through a backward finite difference discretization in time, we define a sequentially implicit time-stepping algorithm that uncouples the system at each time-step. The Galerkin method is employed to approximate the pressure, and accurate velocity approximations are calculated via a post-processing technique involving the conservation of mass and Darcy's law. A stabilized finite element ( SUPG ) method is applied to the convection–diffusion equation delivering stable and accurate solutions. Error estimates with quasi-optimal rates of convergence are derived under suitable regularity hypotheses. Numerical results are presented confirming the predicted rates of convergence for the post-processing technique and illustrating the performance of the proposed methodology when applied to miscible displacements with adverse mobility ratios. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 519–548, 1998 |
