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 definite symmetric part) on the fine 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 fine mesh. 1. Introduction. This paper considers the finite element approximation of the steady state Navier-Stokes equations, modelling the equilibrium flow of a viscous, incompressible fluid: (1:1) 8 ? ? ! ? ? : \Γ \ + u \Δ ru+rp = f ; in\Ω ; r \Δ u = 0; in\Ω ; u = 0 on @\Ω and R pdx = 0: In (1.1),\Ω is a domain in R d ; d = 2 or 3; u :\Ω ! R d is the flow field, p :\...