title: General spline filters for discontinuous Galerkin solutions.
abstract: The discontinuous Galerkin (dG) method outputs a sequence of polynomial pieces. Post-processing the sequence by Smoothness-Increasing Accuracy-Conserving (SIAC) convolution not only increases the smoothness of the sequence but can also improve its accuracy and yield superconvergence. SIAC convolution is considered optimal if the SIAC kernels, in the form of a linear combination of B-splines of degreed, reproduce polynomials of degree 2d. This paper derives simple formulas for computing the optimal SIAC spline coefficients for the general case including non-uniform knots.
authors.affiliation: Dept C.I.S.E., CSE Bldg, University of Florida, Gainesville, FL 32611-6120, United States.
authors.forename: Jörg
authors.initials: J
authors.lastname: Peters
keywords: Filter kernel; Non-uniform B-splines; Polynomial reproduction; Post-processing Discontinuous Galerkin; SIAC convolution