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Journal of Scientific Computing

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01-01-2013

On the Connection Between the Correction and Weighting Functions in the Correction Procedure via Reconstruction Method

Authors: Meilin Yu, Z. J. Wang

Published in: Journal of Scientific Computing | Issue 1/2013

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Abstract

In this note, the connection between the correction and weighting functions for the correction procedure via reconstruction (CPR) method in 1D is addressed. A one-parameter family of weighting functions is constructed from the discontinuous test space. It is found that if the solution polynomials lie in the space P ^k, then the first k weighting functions can always be chosen as the basis of the polynomial space P ^k−1 and the last weighting function can be selected as a piece-wise continuous polynomial. There exists at least one set of weighting functions which can recover the energy stable flux reconstruction (ESFR) schemes. This strategy has been successfully applied to recover several known high-order discontinuous schemes, including DG, SD, SV, and Huynh’s g ₂ scheme.

previous article Quadratic Finite Element Approximations of the Monge-Ampère Equation

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Title: On the Connection Between the Correction and Weighting Functions in the Correction Procedure via Reconstruction Method
Authors: Meilin Yu
Z. J. Wang
Publication date: 01-01-2013
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2013
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9618-3

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