A three-step Oseen correction method for the steady Navier-Stokes equations

We present and analyze a two-grid scheme based on mixed finite element approximations for the steady incompressible Navier-Stokes equations. This numerical scheme aims at the simulations of high Reynolds number flows and consists of three steps: in the first step, we solve a finite element variational multiscale-stabilized nonlinear Navier-Stokes system on a coarse mesh, and then, in the second and third steps, we solve Oseen-linearized and -stabilized problems which have the same stiffness matrices with only different right-hand sides on a fine mesh. We provide error bounds for the approximate solutions, derive algorithmic parameter scalings from the analysis, and present some numerical results to verify the theoretical predictions and demonstrate the effectiveness of the proposed method.