A TWO-GRID METHOD FOR THE STEADY PENALIZED NAVIER-STOKES EQUATIONS

A two-grid method for the steady penalized incompressible Navier-Stokes equations is presented. Convergence results are proved. If $h=O(H^{3-s})$ and $epsilon=O(H^{5-2s}) (s=0 (n=2); s=frac{1}{2} (n=3))$ are chosen, the convergence order of this two-grid method is the same as that of the usual finite element method. Numerical results show that this method is efficient and can save a lot of computation time.