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Symbolic Evaluation of hp ‐FEM Element Matrices
Author(s) -
Haubold Tim,
Pillwein Veronika,
Beuchler Sven
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900446
Subject(s) - ansatz , finite element method , polynomial , mathematics , symbolic computation , element (criminal law) , matrix (chemical analysis) , computation , jacobi polynomials , orthogonal polynomials , pure mathematics , algebra over a field , mathematical analysis , algorithm , physics , materials science , political science , law , mathematical physics , thermodynamics , composite material
In this paper we consider higher order shape functions for finite elements on a triangle. On the reference element Dubiner‐like ansatz functions based on suitable integrated Jacobi polynomials are chosen. It can be proved that the corresponding mass and stiffness matrices are sparse for all polynomial degree p . Due to the orthogonal relations between Jacobi polynomials the exact values of the entries of mass and stiffness matrix can be determined. Using symbolic computation, we can find simple recurrence relations which allow us to compute the remaining nonzero entries in optimal arithmetic complexity.