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On spectral approximations in elliptical geometries using Mathieu functions
Author(s):
Jie
Shen;
Li-Lian
Wang.
Journal:
Math. Comp.
78
(2009),
815-844.
MSC (2000):
Primary 65N35, 65N22, 65F05, 35J05
Posted:
November 20, 2008
MathSciNet review:
2476561
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Abstract:
We consider in this paper approximation properties and applications of Mathieu functions. A first set of optimal error estimates are derived for the approximation of periodic functions by using angular Mathieu functions. These approximation results are applied to study the Mathieu-Legendre approximation to the modified Helmholtz equation and Helmholtz equation. Illustrative numerical results consistent with the theoretical analysis are also presented.
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Additional Information:
Jie
Shen
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
shen@math.purdue.edu
Li-Lian
Wang
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637616, Singapore
Email:
lilian@ntu.edu.sg
DOI:
10.1090/S0025-5718-08-02197-2
PII:
S 0025-5718(08)02197-2
Keywords:
Mathieu functions,
elliptic coordinates,
approximation in Sobolev spaces,
Helmholtz equations
Received by editor(s):
March 4, 2008
Posted:
November 20, 2008
Additional Notes:
The work of the first author was partially supported by NSF Grant DMS-0610646.
The work of the second author was partially supported by a Start-Up grant from NTU, Singapore MOE Grant T207B2202, and Singapore NRF2007IDM-IDM002-010.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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