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A new C~0 discontinuous Galerkin method for Kirchhoff plates

机译:Kirchhoff板的一种新的C〜0不连续Galerkin方法

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摘要

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.
机译:遵循(Castillo等,2000)[10]和(Cockburn,2003)[12]中的一些思想,开发了一种构造C-0不连续伽勒金(CDG)方法的通用框架来解决Kirchhoff板弯曲问题。基于离散的稳定性标识来确定数字迹线,这导致了一类稳定的CDG方法。一种稳定的CDG方法(称为LCDG方法)在我们的研究中特别有趣。它可以看作是对LDG方法的四阶问题的扩展,在(Castillo et al。,2000)[10]和(Cockburn,2003)[12]中进行了研究。对于该方法,建立了某些断能范数和H〜1-范数的最优阶误差估计。报告了一些数值结果,证实了理论收敛阶。

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