High Order Biorthogonal Functions in H (curl)
- authored by
- Tim Haubold, Sven Beuchler, Joachim Schöberl
- 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.
- Organisation(s)
-
Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
- External Organisation(s)
-
University of Göttingen
TU Wien (TUW)
- Type
- Article
- Journal
- SIAM journal on numerical analysis
- Volume
- 62
- Pages
- 2331-2348
- No. of pages
- 18
- ISSN
- 0036-1429
- Publication date
- 14.10.2024
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Numerical Analysis, Computational Mathematics, Applied Mathematics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2310.06986 (Access:
Open)
https://doi.org/10.1137/23M1606794 (Access: Closed)
