Two-level iteration penalty methods for the Navier-Stokes equations with friction boundary conditions (Q2016613)

Summary: 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 \(H\) 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 \(h\). The error estimate obtained in this paper shows that if \(H\), \(h\), and \(\varepsilon\) 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.