This paper presents a two-grid method for solving systems of partial differential
equations modelling free flow coupled with porous media flow. This work considers
both the coupled Stokes and Darcy as well as the coupled Navier-Stokes and Darcy
problems. The numerical schemes proposed are based on combinations of the con-
tinuous finite element method and the discontinuous Galerkin method. Numerical
errors and convergence rates for solutions obtained from the two-grid method are
presented. CPU times for the two-grid algorithm are shown to be significantly less
than those obtained by solving the fully coupled problem.