A two‐grid method with backtracking for the mixed <scp>Navier–Stokes</scp>/Darcy model

Abstract

Abstract 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 both L 2 and H 1 optimal velocity and piezometric head approximations and an L 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.