This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size in combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh size . The error estimate obtained in this paper shows that if , , and can be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.
"Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions." Abstr. Appl. Anal. 2013 1 - 17, 2013. https://doi.org/10.1155/2013/125139