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Volume 25, Issue 3
Non Spurious Spectral-Like Element Methods for Maxwell's Equations

Gary Cohen & Marc Duruflé

J. Comp. Math., 25 (2007), pp. 282-304.

Published online: 2007-06

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  • Abstract

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.

  • Keywords

Maxwell's equations, Discontinuous Galerkin methods, Edge elements, Mass lumping.

  • AMS Subject Headings

65M60, 65M70, 35Q60, 34L16, 65N25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-282, author = {Cohen , Gary and Duruflé , Marc}, title = {Non Spurious Spectral-Like Element Methods for Maxwell's Equations}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {3}, pages = {282--304}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8693.html} }
TY - JOUR T1 - Non Spurious Spectral-Like Element Methods for Maxwell's Equations AU - Cohen , Gary AU - Duruflé , Marc JO - Journal of Computational Mathematics VL - 3 SP - 282 EP - 304 PY - 2007 DA - 2007/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8693.html KW - Maxwell's equations, Discontinuous Galerkin methods, Edge elements, Mass lumping. AB -

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.

Cohen , Gary and Duruflé , Marc. (2007). Non Spurious Spectral-Like Element Methods for Maxwell's Equations. Journal of Computational Mathematics. 25 (3). 282-304. doi:
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