Commun. Comput. Phys., 11 (2012), pp. 863-892.


High-Order Low Dissipation Conforming Finite-Element Discretization of the Maxwell Equations

Sebastien Jund 1, Stephanie Salmon 2, Eric Sonnendrucker 1*

1 IRMA, UMR 7501 Universite de Strasbourg and CNRS, and CALVI project-team, INRIA Nancy Grand Est, 7 rue Rene Descartes, F-67084 STRASBOURG Cedex.
2 Laboratoire de Mathematiques EA 4535, Universite de Reims, U.F.R. Sciences Exactes et Naturelles, Moulin de la Housse - BP 1039, F-51687 REIMS cedex 2.

Received 10 March 2010; Accepted (in revised version) 23 May 2011
Available online 28 October 2011
doi:10.4208/cicp.100310.230511a

Abstract

In this paper, we study high order discretization methods for solving the Maxwell equations on hybrid triangle-quad meshes. We have developed high order finite edge element methods coupled with different high order time schemes and we compare results and efficiency for several schemes. We introduce in particular a class of simple high order low dissipation time schemes based on a modified Taylor expansion.

AMS subject classifications: 65M60

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Key words: Maxwell's equations, edge finite element method, mass lumping, time discretization schemes.

*Corresponding author.
Email: stephanie.salmon@univ-reims.fr (S. Salmon), sonnen@math.unistra.fr (E. Sonnendrucker)
 

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