High order Nédélec elements with local complete sequence properties
ISSN: 0332-1649
Article publication date: 1 June 2005
Abstract
Purpose
The goal of the presented work is the efficient computation of Maxwell boundary and eigenvalue problems using high order H(curl) finite elements.
Design/methodology/approach
Discusses a systematic strategy for the realization of arbitrary order hierarchic H(curl)‐conforming finite elements for triangular and tetrahedral element geometries. The shape functions are classified as lowest order Nédélec, higher‐order edge‐based, face‐based (only in 3D) and element‐based ones.
Findings
Our new shape functions provide not only the global complete sequence property but also local complete sequence properties for each edge‐, face‐, and element‐block. This local property allows an arbitrary variable choice of the polynomial degree for each edge, face, and element. A second advantage of this construction is that simple block‐diagonal preconditioning gets efficient. Our high order shape functions contain gradient shape functions explicitly. In the case of a magnetostatic boundary value problem, the gradient basis functions can be skipped, which reduces the problem size, and improves the condition number.
Originality/value
Successfully applies the new high order elements for a 3D magnetostatic boundary value problem, and a Maxwell eigenvalue problem showing severe edge and corner singularities.
Keywords
Citation
Schöberl, J. and Zaglmayr, S. (2005), "High order Nédélec elements with local complete sequence properties", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 2, pp. 374-384. https://doi.org/10.1108/03321640510586015
Publisher
:Emerald Group Publishing Limited
Copyright © 2005, Emerald Group Publishing Limited