Details
| Original language | English |
|---|---|
| Article number | 32 |
| Number of pages | 17 |
| Journal | Mathematics in Computer Science |
| Volume | 16 |
| Issue number | 4 |
| Early online date | 13 Dec 2022 |
| Publication status | Published - Dec 2022 |
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.
Keywords
- High order finite element methods, Holonomic systems, Orthogonal polynomials, Recurrence equations
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Mathematics in Computer Science, Vol. 16, No. 4, 32, 12.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Recurrences for Quadrilateral High-Order Finite Elements
AU - Beuchler, Sven
AU - Haubold, Tim
AU - Pillwein, Veronika
N1 - Funding Information: The work of the first author is funded by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453).
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - High order finite element methods
KW - Holonomic systems
KW - Orthogonal polynomials
KW - Recurrence equations
UR - http://www.scopus.com/inward/record.url?scp=85144370019&partnerID=8YFLogxK
U2 - 10.1007/s11786-022-00547-2
DO - 10.1007/s11786-022-00547-2
M3 - Article
AN - SCOPUS:85144370019
VL - 16
JO - Mathematics in Computer Science
JF - Mathematics in Computer Science
SN - 1661-8270
IS - 4
M1 - 32
ER -