Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 759547, 20 pages
doi:10.1155/2010/759547
Research Article

On the Local Discontinuous Galerkin Method for Linear Elasticity

Yuncheng Chen,1 Jianguo Huang,1,2 Xuehai Huang,1 and Yifeng Xu1

1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2Division of Computational Science, E-Institute of Shanghai Universities and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, China

Received 25 February 2010; Accepted 22 May 2010

Academic Editor: Angelo Luongo

Copyright © 2010 Yuncheng Chen 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

Following Castillo et al. (2000) and Cockburn (2003), a general framework of constructing discontinuous Galerkin (DG) methods is developed for solving the linear elasticity problem. The numerical traces are determined in view of a discrete stability identity, leading to a class of stable DG methods. A particular method, called the LDG method for linear elasticity, is studied in depth, which can be viewed as an extension of the LDG method discussed by Castillo et al. (2000) and Cockburn (2003). The error bounds in L2-norm, H1-norm, and a certain broken energy norm are obtained. Some numerical results are provided to confirm the convergence theory established.