Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle

Author(s): Huiyuan Li; Jie Shen.
Journal: Math. Comp. 79 (2010), 1621-1646.
MSC (2000): Primary 65N35, 65N22, 65F05, 35J05
Posted: September 17, 2009
MathSciNet review: 2630005
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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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