Essentially nonoscillatory spectral Fourier methods for shock wave calculations

Authors:
Wei Cai, David Gottlieb and Chi-Wang Shu

Journal:
Math. Comp. **52** (1989), 389-410

MSC:
Primary 65M99

MathSciNet review:
955749

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Abstract: In this paper, we present an essentially nonoscillatory spectral Fourier method for the solution of hyperbolic partial differential equations. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that essentially no oscillations develop in the solution. Also, the accuracy of the spectral solution of the inviscid Burgers equation is shown to be higher than a fixed order.

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0955749-2

Article copyright:
© Copyright 1989
American Mathematical Society