Computing SIAC spline coefficients

2014/10/01 by Peters, Jörg
#41A15 65D07 #F.2.1 #FOS: Mathematics #G.1.2 #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1410.0325

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.

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