Filtering in Legendre spectral methods

Hesthaven, Jan; Kirby, Robert

doi:10.1090/S0025-5718-08-02110-8

Filtering in Legendre spectral methods
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by Jan S. Hesthaven and Robert M. Kirby;

Math. Comp. 77 (2008), 1425-1452

DOI: https://doi.org/10.1090/S0025-5718-08-02110-8

Published electronically: March 5, 2008

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Abstract:

We discuss the impact of modal filtering in Legendre spectral methods, both on accuracy and stability. For the former, we derive sufficient conditions on the filter to recover high order accuracy away from points of discontinuity. Computational results confirm that less strict necessary conditions appear to be adequate. We proceed to discuss a instability mechanism in polynomial spectral methods and prove that filtering suffices to ensure stability. The results are illustrated by computational experiments.

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