Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations

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(vertical bar logh vertical bar H-1/2(3)). These methods we studied provide an approximate solution ((u) over tilde (v)(h), (p) over tilde (v)(h)) 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.