ISSN:
1573-7691
Keywords:
Spectral method
;
accuracy
;
Gibbs phenomenon
;
nonlinear conservation laws
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract 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 PDE with discontinuous solutions, Fourier spectral method will produce 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 have found out that the moments against analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a Gegenbauer polynomial based post-processing.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02091780
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