Abstract: 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 point sets that aim to minimise the L
∞ error of an associated interpolating polynomial. The present work combines a comprehensive review of known approximation theory results, with new results, and numerical experiments, to motivate that in fact point sets for FR should aim to minimise the L
2 error of an associated interpolating polynomial. New results include identification of a nodal point set that minimises the L
2 norm of an interpolating polynomial, and a proof of the equivalence between such an interpolating polynomial and an L
2 approximating polynomial with coefficients obtained using a Gauss-Legendre quadrature rule. Numerical experiments confirm that FR errors can be reduced by an order-of-magnitude by switching from popular point sets such as Chebyshev, Chebyshev-Lobatto and Legendre-Lobatto to Legendre point sets.
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