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 re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.

中文翻译：

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节点间断Galerkin方法的稳定滤波过程

我们证明了用于节点不连续伽勒金（DG）方法的最常见的滤波过程是稳定的。该证明利用DG逼近是由多项式基函数构造的，并且积分是通过高阶准确的Legendre-Gauss-Lobatto正交来逼近的。理论讨论将有限差分法的稳定滤波结果重新关联到DG设置中。数值测试验证并验证了基础理论结果。