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Abstract and Applied Analysis
Volume 2013, Article ID 125139, 17 pages
Research Article

Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions

College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China

Received 2 April 2013; Revised 12 June 2013; Accepted 19 June 2013

Academic Editor: Stanislaw Migorski

Copyright © 2013 Yuan Li and Rong An. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.