A two-grid method with backtracking for the mixedNavier-Stokes/Darcy model

In this paper, we consider the effect of adding a coarse mesh correction to the two-grid algorithm for the mixed Navier-Stokes/Darcy model. The method yields bothL(2)andH(1)optimal velocity and piezometric head approximations and anL(2)optimal pressure approximation. The method involves solving one small, coupled, nonlinear coarse mesh problem, two independent subproblems (linear Navier-Stokes equation and Darcy equation) on the fine mesh, and a correction problem on the coarse mesh. Theoretical analysis and numerical tests are done to indicate the significance of this method.