A practical assessment of spectral accuracy for hyperbolic problems with discontinuities (Q1116672)

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 \textit{D. Gottlieb} and \textit{E. Tadmor} [Proc. U.S.-Israel Workshop, Jerusalem 1984, Proc. Sci. Comput. 6, 357-375 (1985; Zbl 0597.65099)].