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  =  ϵ 1 / 4 h 1 / 2 , a large penalty Stokes problem on a fine mesh with mesh size h , where 0 <  ϵ  < 1 is a penalty parameter. The method we study provides an approximate solutionu ϵ h , p ϵ hwith the convergence rate of same order as the penalty finite volume solution ( u ϵh , p ϵh ), 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 © 2013 John Wiley & Sons, Ltd.