Computing SIAC spline coefficients

Abstract

The Discontinuous Galerkin (DG) method applied to hyperbolic differential equations outputs weakly-linked polynomial pieces. Post-processing these pieces by Smoothness-Increasing Accuracy-Conserving (SIAC) convolution with B-splines can improve the accuracy of the output and yield superconvergence. SIAC convolution is considered optimal if the SIAC kernels, in the form of a linear combinations of B-splines of degree d, reproduce polynomials of degree 2d. This paper derives simple formulas for computing the optimal SIAC spline coefficients.