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Spectral Approximations on the Triangle

R. G. Owens
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 454, No. 1971 (Mar. 8, 1998), pp. 857-872
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/53157
Page Count: 16
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Spectral Approximations on the Triangle
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Abstract

In this paper we describe a new family of polynomials which are eigenfunctions of a singular Sturm-Liouville problem on the triangle T2 = {(x,y): x ≥ 0, y ≥ 0, x + y ≤ 1}. The polynomials are shown to be orthogonal over T2 with respect to a unit weight function, and may be used in approximations which are exponentially convergent for functions which are infinitely smooth in T2. The zeros of the polynomials may be used in cubature formulae on T2.

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