A new C-0 discontinuous Galerkin method for Kirchhoff plates

作者：Huang, Jianguo; Huang, Xuehai; Han, Weimin^*

来源：Computer Methods in Applied Mechanics and Engineering, 2010, 199(23-24): 1446-1454.

DOI：10.1016/j.cma.2009.12.012

• Kirchhoff plate
• C-0 discontinuous Galerkin method
• Numerical trace
• LCDG method
• Error analysis

A general framework of constructing C-0 discontinuous Galerkin (CDG) methods is developed for solving the Kirchhoff plate bending problem, following some ideas in (Castillo et al., 2000) [10] and (Cockburn, 2003) [12]. The numerical traces are determined based on a discrete stability identity, which lead to a class of stable CDG methods. A stable CDG method, called the LCDG method, is particularly interesting in our study. It can be viewed as an extension to fourth-order problems of the LDG method studied in (Castillo et al., 2000) [10] and (Cockburn, 2003) [12]. For this method, optimal order error estimates in certain broken energy norm and H-1-norm are established. Some numerical results are reported, confirming the theoretical convergence orders.

• 出版日期2010
• 单位上海大学; 上海交通大学; 上海师范大学