Two-level stabilized nonconforming finite element method for the Stokes equations

summary:In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the $NCP_{1}-P_{1}$ pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size $H$ and a large stabilized Stokes problem on a fine mesh size $h=H/3$. Numerical results are presented to show the convergence performance of this combined algorithm