Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 570980, 18 pages
http://dx.doi.org/10.1155/2011/570980
Research Article

An Optimal Error Estimates of 𝐻 1 -Galerkin Expanded Mixed Finite Element Methods for Nonlinear Viscoelasticity-Type Equation

Haitao Che,1,2 Yiju Wang,1 and Zhaojie Zhou3

1School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, China
2School of Mathematics and Information Science, Weifang University, Weifang, Shandong 261000, China
3School of Mathematical Sciences, Shandong Normal University, Jinan, Shandong 250014, China

Received 30 March 2011; Revised 14 August 2011; Accepted 21 August 2011

Academic Editor: Ben T. Nohara

Copyright © 2011 Haitao Che 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

We investigate a 𝐻 1 -Galerkin mixed finite element method for nonlinear viscoelasticity equations based on 𝐻 1 -Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.