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

摘要

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 = ?μ~1 / 4_h~(1 / 2), a large penalty Stokes problem on a fine mesh with mesh size h, where 0 < ?μ < 1 is a penalty parameter. The method we study provides an approximate solution u?μh,p?μh with the convergence rate of same order as the penalty finite volume solution (u?_(μh),p _(?μh)), 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.