Filtering in Legendre spectral methods

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 a...

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Bibliographic Details
Published in:Mathematics of computation 2008-09, Vol.77 (263), p.1425-1452
Main Authors: Hesthaven, Jan S., Kirby, Robert M.
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Exact sciences and technology
Legendre polynomials
Mathematical functions
Mathematical robustness
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Optical filters
Polynomials
Sciences and techniques of general use
Spectral methods
Spectroscopic analysis
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-08-02110-8