Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65M70, 65M12

Retrieve articles in all journals with MSC (2000): 65M70, 65M12

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.

American Mathematical Society