Overview

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials. Shu, Chi-Wang and Wong, Peter S. Unspecified Center AD-A284063, NASA-CR-194959, NAS 1.26:194959, ICASE-94-67 NAS1-19480; DAAL03-91-G-0123; DAAH04-94-G-0205; NSF DMS-92-11820; AF-AFOSR-0090-93; NAG1-1145; RTOP 505-90-52-01...

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9781725009035

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