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On the Local Discontinuous Galerkin Method for Linear Elasticity

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Listed:
  • Yuncheng Chen
  • Jianguo Huang
  • Xuehai Huang
  • Yifeng Xu

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

Suggested Citation

  • Yuncheng Chen & Jianguo Huang & Xuehai Huang & Yifeng Xu, 2010. "On the Local Discontinuous Galerkin Method for Linear Elasticity," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-20, July.
    • Handle: RePEc:hin:jnlmpe:759547
    DOI: 10.1155/2010/759547
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