论文标题
淋巴结不连续的Galerkin方法的稳定过滤程序
Stable filtering procedures for nodal discontinuous Galerkin methods
论文作者
论文摘要
我们证明，淋巴结不连续的Galerkin（DG）方法最常见的过滤过程是稳定的。证明DG近似是由多项式基础函数构建的，并且积分与高阶精确的Legendre-Gauss-lobatto Quadrature近似。理论讨论可将有限差异方法的稳定过滤结果重新定义为DG设置。结果表明，过滤的稳定性等于从所谓的传输问题分析中借来的特定合同条件。因此，时间稳定性证明依赖于以下事实：问题的基本空间离散化在溶液上具有半差异。提供数值测试以验证和验证基本的理论结果。
We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre-Gauss-Lobatto quadrature. The theoretical discussion serves to re-contextualize stable filtering results for finite difference methods into the DG setting. It is shown that the stability of the filtering is equivalent to a particular contractivity condition borrowed from the analysis of so-called transmission problems. As such, the temporal stability proof relies on the fact that the underlying spatial discretization of the problem possesses a semi-discrete bound on the solution. Numerical tests are provided to verify and validate the underlying theoretical results.
