Non-Spurious Spectral Like Element Methods for Maxwell's equations

Gary Cohen (1) , Marc Duruflé (2, 3)

1 INRIA Rocquencourt
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
3 IMB - Institut de Mathématiques de Bordeaux

In this paper, we give the state of the art for the so called "mixed spectral elements" for Maxwell's equations. Several families of elements, such as edge elements and discontinuous Galerkin methods (DGM) are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is a novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements.

Domains: Mathematics [math]; Analysis of PDEs [math.AP]

Gary Cohen, Marc Duruflé. Non-Spurious Spectral Like Element Methods for Maxwell's equations. Journal of Computational Mathematics -International Edition-, 2007, pp.282-304. ⟨hal-00385458⟩