High Order Biorthogonal Functions in H (curl)

verfasst von

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.

Organisationseinheit(en)

Institut für Angewandte Mathematik
PhoenixD: Simulation, Fabrikation und Anwendung optischer Systeme

Externe Organisation(en)

Georg-August-Universität Göttingen
Technische Universität Wien (TUW)

Typ

Artikel

Journal

SIAM journal on numerical analysis

Band

62

Seiten

2331-2348

Anzahl der Seiten

18

ISSN

0036-1429

Publikationsdatum

14.10.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Numerische Mathematik, Computational Mathematics, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2310.06986 (Zugang: Offen)
https://doi.org/10.1137/23M1606794 (Zugang: Geschlossen)