(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
In this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size h=O(H^2) or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size h=O(|h|^1/2H^3). These methods we studied provide an approximate solution (u_h^v,p_h^v) with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.