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Mathematics of Computation

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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
Published electronically: March 5, 2008
MathSciNet review: 2398775
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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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Additional Information

Jan S. Hesthaven
Affiliation: Division of Applied Mathematics, Brown University, Box F, Providence, Rhode Island 02912

Robert M. Kirby
Affiliation: School of Computing, University of Utah, Salt Lake City, Utah 84112

Keywords: Spectral methods, filtering, stabilization, Legendre polynomials
Received by editor(s): January 2, 2004
Received by editor(s) in revised form: July 21, 2004
Published electronically: March 5, 2008
Additional Notes: The work of the first author was partly supported by NSF Career Award DMS-0132967, NSF International Award INT-0307475, ARO under contract DAAD19-01-1-0631, and the Alfred P. Sloan Foundation through a Sloan Research Fellowship.
The work of the second author was supported by NSF Career Award NSF-CCF0347791.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.