Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Filtering in Legendre spectral methods

Authors: Jan S. Hesthaven and Robert M. Kirby
Journal: Math. Comp. 77 (2008), 1425-1452
MSC (2000): Primary 65M70; Secondary 65M12
Posted: March 5, 2008
MathSciNet review: 2398775
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Abstract | References | Similar Articles | Additional Information

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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