Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

Abstract We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits DG approximation constructed from polynomial basis functions and integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. theoretical discussion re-contextualizes stable results finite difference into setting. Numerical tests verify validate underlying results.