Abstract
Numerical experiments are performed to compare the accuracy obtained when physical and transform space filters are used to smooth the oscillations in Fourier collocation approximations to discontinuous solutions of a linear wave equation. High-order accuracy can be obtained away from a discontinuity but the order is strongly filter dependent. Polynomial order accuracy is demonstrated when smooth high-order Fourier filters are used. Spectral accuracy is obtained with the physical space filter of Gottlieb and Tadmor.
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Kopriva, D.A. A practical assessment of spectral accuracy for hyperbolic problems with discontinuities. J Sci Comput 2, 249–262 (1987). https://doi.org/10.1007/BF01061112
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DOI: https://doi.org/10.1007/BF01061112