Recurrence Relations for a Family of Orthogonal Polynomials on a Triangle-Reference-Cited by-同舟云学术

Recurrence Relations for a Family of Orthogonal Polynomials on a Triangle

Published:2020 Issue: Volume: Page:79-92
ISSN:1439-7358
Container-title:Lecture Notes in Computational Science and Engineering
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Author:

Olver Sheehan,Townsend Alex,Vasil Geoffrey M.

Abstract

AbstractThis paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partial derivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in a systematic fashion by introducing ladder operators that map an orthogonal polynomial to another by incrementing or decrementing its associated parameters by one. We apply the results to efficiently calculating the Laplacian of polynomial approximations of functions on the triangle, using polynomial degrees in the thousands, i.e., millions of degrees of freedom.

Publisher

Springer International Publishing

Link

https://link.springer.com/content/pdf/10.1007/978-3-030-39647-3_5

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