On the Local Discontinuous Galerkin Method for Linear Elasticity. (12th July 2010)

• Record Type: Journal Article
• Authors: Chen, Yuncheng; Huang, Jianguo; Huang, Xuehai; Xu, Yifeng
• Other Names: Luongo Angelo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2010(2010)
• Publication Date: 2010-07-12
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2010/759547
• Languages: English
• ISSNs: 1024-123X

Abstract

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 L 2 -norm, H 1 -norm, and a certain broken energy norm are obtained. Some numerical results are provided to confirm the convergence theory established.