How to Design a Generic Accuracy-Enhancing Filter for Discontinuous Galerkin Methods

Higher order accuracy is one of the well-known beneficial properties discontinuous Galerkin (DG) method. Furthermore, many studies have demonstrated superconvergence property semi-discrete DG One can take advantage this by post-processing techniques to enhance solution. The smoothness-increasing accuracy-conserving (SIAC) filter a popular technique introduced Cockburn et al. (Math. Comput. 72(242): 577–606, 2003). It raise convergence rate solution (with polynomial degree k) from $$k+1$$ $$2k+1$$ in $$L^2$$ norm. This paper first investigates general basis functions used construct SIAC for extraction. generic function framework relaxes structure and provides flexibility more intricate features, such as extra smoothness. Second, we study distribution propose new called compact that significantly reduces support size original while preserving (or even improving) its ability We prove error estimate filters. Numerical results are presented confirm theoretical demonstrate performance