author = {Haubold Tim and Pillwein Veronika and Beuchler Sven},
title = {{Symbolic Evaluation of hp-FEM Element Matrices}},
booktitle = {{Proceedings in Applied Mathematics and Mechanics (PAMM)}},
language = {english},
abstract = {Abstract 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.},
volume = {19},
number = {1},
pages = {e201900446--e2019004},
isbn_issn = {?},
year = {2019},
editor = {Gesellschaft für Angewandte Mathematik und Mechanik (GAMM)},
refereed = {yes},
length = {2},
conferencename = {2019 Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201900446}