On nodal point sets for flux reconstruction

Nodal point sets, and associated collocation projections, play an important role in a range of high-order methods, including Flux Reconstruction (FR) schemes. Historically, efforts have focused on identifying nodal sets that aim to minimise the L∞ error interpolating polynomial. The present work combines comprehensive review known approximation theory results, with new numerical experiments, motivate fact for FR should L2 New results include identification set minimises norm polynomial, proof equivalence between such polynomial approximating coefficients obtained using Gauss–Legendre quadrature rule. Numerical experiments confirm errors can be reduced by order-of-magnitude switching from popular as Chebyshev, Chebyshev–Lobatto Legendre–Lobatto Legendre sets.