Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 2331-2348 |
| Seitenumfang | 18 |
| Fachzeitschrift | SIAM journal on numerical analysis |
| Jahrgang | 62 |
| Ausgabenummer | 5 |
| Publikationsstatus | Veröffentlicht - 14 Okt. 2024 |
Abstract
From the literature, it is known that the choice of basis functions in hp-FEM heavily influences the computational cost in order to obtain an approximate solution. Depending on the choice of the reference element, suitable tensor product like basis functions of Jacobi polynomials with different weights lead to optimal properties due to condition number and sparsity. This paper presents biorthogonal basis functions to the primal basis functions mentioned above. The authors investigate hypercubes and simplices as reference elements, as well as the cases of H1 and H(Curl). The functions can be expressed as sums of tensor products of Jacobi polynomials with maximal two summands.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Numerische Mathematik
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: SIAM journal on numerical analysis, Jahrgang 62, Nr. 5, 14.10.2024, S. 2331-2348.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - High Order Biorthogonal Functions in H (curl)
AU - Haubold, Tim
AU - Beuchler, Sven
AU - Schöberl, Joachim
N1 - Publisher Copyright: © 2024 SIAM.
PY - 2024/10/14
Y1 - 2024/10/14
N2 - From the literature, it is known that the choice of basis functions in hp-FEM heavily influences the computational cost in order to obtain an approximate solution. Depending on the choice of the reference element, suitable tensor product like basis functions of Jacobi polynomials with different weights lead to optimal properties due to condition number and sparsity. This paper presents biorthogonal basis functions to the primal basis functions mentioned above. The authors investigate hypercubes and simplices as reference elements, as well as the cases of H1 and H(Curl). The functions can be expressed as sums of tensor products of Jacobi polynomials with maximal two summands.
AB - From the literature, it is known that the choice of basis functions in hp-FEM heavily influences the computational cost in order to obtain an approximate solution. Depending on the choice of the reference element, suitable tensor product like basis functions of Jacobi polynomials with different weights lead to optimal properties due to condition number and sparsity. This paper presents biorthogonal basis functions to the primal basis functions mentioned above. The authors investigate hypercubes and simplices as reference elements, as well as the cases of H1 and H(Curl). The functions can be expressed as sums of tensor products of Jacobi polynomials with maximal two summands.
KW - finite elements
KW - numerical methods for partial differential equations
KW - orthogonal polynomials
UR - http://www.scopus.com/inward/record.url?scp=85209680203&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2310.06986
DO - 10.48550/arXiv.2310.06986
M3 - Article
AN - SCOPUS:85209680203
VL - 62
SP - 2331
EP - 2348
JO - SIAM journal on numerical analysis
JF - SIAM journal on numerical analysis
SN - 0036-1429
IS - 5
ER -