Error estimates for two-level penalty finite volume method for the stationary Navier-Stokes equations

Two-level penalty finite volume method for the stationary Navier-Stokes equations based on the P-1 - P-0 element is considered in this paper. The method involves solving one small penalty Navier-Stokes problem on a coarse mesh with mesh size H = epsilon(1/4)h(1/2), a large penalty Stokes problem on a fine mesh with mesh size h, where 0 < epsilon < 1 is a penalty parameter. The method we study provides an approximate solution (u(epsilon)(h), p(epsilon)(h)) with the convergence rate of same order as the penalty finite volume solution (u(epsilon h), p(epsilon h)), which involves solving one large penalty Navier-Stokes problem on a fine mesh with the same mesh size h. However, our method can save a large amount of computational time. Copyright (C) 2013 John Wiley & Sons, Ltd.