## Abstract and Applied Analysis

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

#### Abstract

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 $\epsilon$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 125139, 17 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511973

Digital Object Identifier
doi:10.1155/2013/125139

Mathematical Reviews number (MathSciNet)
MR3081589

Zentralblatt MATH identifier
1299.76143

#### Citation

Li, Yuan; An, Rong. Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions. Abstr. Appl. Anal. 2013 (2013), Article ID 125139, 17 pages. doi:10.1155/2013/125139. https://projecteuclid.org/euclid.aaa/1393511973

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