A Two-level Method with Backtracking for the Navier-stokes Equations

We consider a two-level method for discretization and solution of the equilibrium Navier-Stokes equations. The method yields an L 2 and H 1 optimal velocity approximation and an L 2 optimal pressure approximation. The 2-level method involves solving one small, nonlinear coarse mesh system, one Oseen problem (hence linear with positive deenite symmetric part) on the ne mesh and one linear correction problem on the coarse mesh. The analysis of the method is complicated by the fact that the corrected approximation is not discretely divergence free on the ne mesh.