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Mathematics in Computer Science
Erschienen in: Mathematics in Computer Science 4/2022

01.12.2022

Recurrences for Quadrilateral High-Order Finite Elements

verfasst von: Sven Beuchler, Tim Haubold, Veronika Pillwein

Erschienen in: Mathematics in Computer Science | Ausgabe 4/2022

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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.
Vorheriger Artikel Memories of Vladimir Gerdt
Nächster Artikel Applications of Bar Code to Involutive Divisions and a “Greedy” Algorithm for Complete Sets

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Fußnoten
1
In practice this usually means p less than about four, due to the resulting condition number and numerical integration.
 
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Metadaten
Titel
Recurrences for Quadrilateral High-Order Finite Elements
verfasst von
Sven Beuchler
Tim Haubold
Veronika Pillwein
Publikationsdatum
01.12.2022
Verlag
Springer International Publishing
Erschienen in
Mathematics in Computer Science / Ausgabe 4/2022
Print ISSN: 1661-8270
Elektronische ISSN: 1661-8289
DOI
https://doi.org/10.1007/s11786-022-00547-2

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