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Advances in Numerical Analysis
Volume 2010 (2010), Article ID 419021, 21 pages
http://dx.doi.org/10.1155/2010/419021
Research Article

Discontinuous Time Relaxation Method for the Time-Dependent Navier-Stokes Equations

Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, USA

Received 17 July 2010; Accepted 16 September 2010

Academic Editor: William John Layton

Copyright © 2010 Monika Neda. 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.

Abstract

A high-order family of time relaxation models based on approximate deconvolution is considered. A fully discrete scheme using discontinuous finite elements is proposed and analyzed. Optimal velocity error estimates are derived. The dependence of these estimates with respect to the Reynolds number Re is π’ͺ ( R e 𝑒 R e ) , which is an improvement with respect to the continuous finite element method where the dependence is π’ͺ ( R e 𝑒 R e 3 ) .