Essentially nonoscillatory spectral Fourier methods for shock wave calculations

Cai, Wei; Gottlieb, David; Shu, Chi-Wang

doi:10.1090/S0025-5718-1989-0955749-2

Essentially nonoscillatory spectral Fourier methods for shock wave calculations
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by Wei Cai, David Gottlieb and Chi-Wang Shu PDF

Math. Comp. 52 (1989), 389-410 Request permission

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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Trigonometric Series