Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 689804, 25 pages
http://dx.doi.org/10.1155/2011/689804
Research Article

A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation

Yunzhang Zhang,1,2 Yanren Hou,1 and Ganshan Yang3,4

1School of Science, Xi'an Jiaotong University, Xi'an 710049, China
2School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China
3Institute of Mathematics Science, Yunnan Normal University, Kunming 650092, China
4Department of Mathematics, Yunnan Nationalities University, Kunming 650031, China

Received 22 November 2010; Revised 13 March 2011; Accepted 29 April 2011

Academic Editor: M. De la Sen

Copyright © 2011 Yunzhang Zhang et al. 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 defect-correction mixed finite element method for solving the time-dependent Johnson-Segalman viscoelastic equations in two dimensions is given. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the resulting residual is corrected in the correction step on the same grid. A streamline upwind Petrov-Galerkin (SUPG) approximation is used to stabilize the hyperbolic character of the constitutive equation for the stress. We establish a priori error estimates for the defect step and the first correction step of the defect correction method. The derived theoretical results are supported by numerical tests.