Recurrences for Quadrilateral High-Order Finite Elements

authored by

Sven Beuchler, Tim Haubold, Veronika Pillwein

Abstract

High order finite element methods (FEM) are well established numerical techniques for solving partial differential equations on complicated domains. In particular, if the unknown solution is smooth, using polynomial basis functions of higher degree speeds up the numerical solution significantly. At the same time, the computations get much more involved and any simplification, such as efficient recurrence relations, are most welcome. Recently, computer algebra algorithms have been applied to improve FEMs in several ways. In this note, we present a symbolic approach to an issue occuring when working with quadrilateral elements.

Organisation(s)

Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines

External Organisation(s)

Johannes Kepler University of Linz (JKU)

Type

Article

Journal

Mathematics in Computer Science

Volume

16

No. of pages

17

ISSN

1661-8270

Publication date

12.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Computational Mathematics, Computational Theory and Mathematics, Applied Mathematics

Electronic version(s)

https://doi.org/10.1007/s11786-022-00547-2 (Access: Closed)