Two- and three-field formulations for wave transmission between media with opposite sign dielectric constants

Anne-Sophie Bonnet-Ben Dhia 1 Patrick Ciarlet 1 Carlo Maria Zwölf 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We consider a simplified scalar model problem related to Maxwell equations, involving wave transmission between media with opposite sign dielectric and/or magnetic constants. We build two variational formulations equivalent to the model problem. We show that, under some suitable conditions, both formulations are well-posed since they fit into the coercive plus compact framework. Advantages over previous studies is the validity of the formulations in the general case of Lipschitz interface between the two media and L∞ dielectric and magnetic constants. An interesting feature of these formulations is that they allow a simple finite element numerical implementation. © 2006 Elsevier B.V. All rights reserved.
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Submitted on : Friday, October 25, 2013 - 10:41:09 AM
Last modification on : Thursday, February 7, 2019 - 5:50:44 PM

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Anne-Sophie Bonnet-Ben Dhia, Patrick Ciarlet, Carlo Maria Zwölf. Two- and three-field formulations for wave transmission between media with opposite sign dielectric constants. Journal of Computational and Applied Mathematics, Elsevier, 2007, 204 (2 SPEC. ISS.), pp.408-417. ⟨10.1016/j.cam.2006.01.046⟩. ⟨hal-00876230⟩

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