Imperial College London
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Professor Peter Vincent

Faculty of Engineering, Department of Aeronautics

Professor of Computational Fluid Dynamics
 
 
 
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Contact

 

+44 (0)20 7594 1975p.vincent

 
 
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Location

 

211City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Witherden:2021:10.1016/j.cam.2020.113014,
author = {Witherden, F and Vincent, P},
doi = {10.1016/j.cam.2020.113014},
journal = {Journal of Computational and Applied Mathematics},
pages = {1--14},
title = {On nodal point sets for Flux Reconstruction},
url = {http://dx.doi.org/10.1016/j.cam.2020.113014},
volume = {381},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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 L² error of an associated interpolating polynomial. New results include identification of a nodal point set that minimises the L² norm of an interpolating polynomial, and a proof of the equivalence between such an interpolating polynomial and an L² approximating polynomial with coefficients obtained using a Gauss–Legendre quadrature rule. Numerical experiments confirm that FR errors can be reduced by an order-ofmagnitude by switching from popular point sets such as Chebyshev, Chebyshev–Lobatto and Legendre–Lobatto to Legendre point sets.
AU  - Witherden,F
AU  - Vincent,P
DO  - 10.1016/j.cam.2020.113014
EP  - 14
PY  - 2021///
SN  - 0377-0427
SP  - 1
TI  - On nodal point sets for Flux Reconstruction
T2  - Journal of Computational and Applied Mathematics
UR  - http://dx.doi.org/10.1016/j.cam.2020.113014
UR  - https://www.sciencedirect.com/science/article/pii/S0377042720303058?via%3Dihub
UR  - http://hdl.handle.net/10044/1/79362
VL  - 381
ER  -
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