  This article considers the application of Smoothness-Increasing
Accuracy-Conserving (SIAC) filtering for the non-linear stabilization of
discontinuous Galerkin (DG) discretizations via entropy correction. Upon
constructing discrete filters from continuous convolution SIAC kernels, the
schemes are made to be conservative and are then appended to the DG method in a
semi-discrete fashion. Performance of these tunable SIAC filters is compared to
the local averaging typically employed in the entropy correction of finite
element methods, and their capabilities are demonstrated for energy
conservation as well as a shock regularization strategy based on an artificial
viscosity estimate. Relaxation Runge-Kutta time integration methods are further
employed in order to ensure a fully-discrete energy preserving procedure, with
impacts of the overall solution accuracy being investigated for calculations of
the one- and two-dimensional Burgers equation.
