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Abstract and Applied Analysis
Volume 2012, Article ID 475801, 23 pages
http://dx.doi.org/10.1155/2012/475801
Research Article

The Backward Euler Fully Discrete Finite Volume Method for the Problem of Purely Longitudinal Motion of a Homogeneous Bar

School of Mathematical Sciences, Shandong Normal University, Jinan, Shandong 250014, China

Received 28 September 2012; Accepted 29 November 2012

Academic Editor: Xiaodi Li

Copyright © 2012 Ziwen Jiang and Deren Xie. 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 present a linear backward Euler fully discrete finite volume method for the initial-boundary-value problem of purely longitudinal motion of a homogeneous bar and an give optimal order error estimates in and norms. Furthermore, we obtain the superconvergence error estimate of the generalized projection of the solution in norm. Numerical experiment illustrates the convergence and stability of this scheme.