Recurrence relations for a family of orthogonal polynomials on a triangle

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Title: Recurrence relations for a family of orthogonal polynomials on a triangle
Authors: Olver, S
Townsend, A
Vasil, G
Item Type: Conference Paper
Abstract: This paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partialderivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in asystematic fashion by introducing ladder operators that map an orthogonal polynomial to another by incrementingor decrementing its associated parameters by one. We apply the results to efficiently calculating the Laplacian ofpolynomial approximations of functions on the triangle, using polynomial degrees in the thousands, i.e., millions ofdegrees of freedom.
Issue Date: 9-Jul-2018
Date of Acceptance: 5-Apr-2019
ISSN: 1439-7358
Publisher: Springer Verlag
Journal / Book Title: Lecture Notes in Computational Science and Engineering
Conference Name: ICOSAHOM 2018
Publication Status: Accepted
Start Date: 2018-07-09
Finish Date: 2018-07-13
Conference Place: London, UK
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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