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Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle
Author(s):
Huiyuan
Li;
Jie
Shen.
Journal:
Math. Comp.
MSC (2000):
Primary 65N35, 65N22, 65F05, 35J05
Posted:
September 17, 2009
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Abstract:
Spectral approximations on the triangle by orthogonal polynomials are studied in this paper. Optimal error estimates in weighted semi-norms for both the  and  orthogonal polynomial projections are established by using the generalized Koornwinder polynomials and the properties of the Sturm-Liouville operator on the triangle. These results are then applied to derive error estimates for the spectral-Galerkin method for second- and fourth-order equations on the triangle. The generalized Koornwinder polynomials and approximation results developed in this paper will be useful for many other applications involving spectral and spectral-element approximations in triangular domains.
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Additional Information:
Huiyuan
Li
Affiliation:
Institute of Software, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
Jie
Shen
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana, 47907
DOI:
10.1090/S0025-5718-09-02308-4
PII:
S 0025-5718(09)02308-4
Keywords:
Orthogonal polynomials,
Koornwinder polynomials,
error estimate,
spectral method
Received by editor(s):
August 12, 2008
Received by editor(s) in revised form:
June 1, 2009
Posted:
September 17, 2009
Additional Notes:
The first author was partially supported by the NSFC grants 10601056, 10431050 and 60573023.
The second author was partially supported by the NFS grant DMS-0610646 and AFOSR FA9550-08-1-0416.
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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