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

Authors:
A. S. Bonnet-Ben Dhia;P. Ciarlet Jr.;C. M. Zwölf
Affiliations:
CNRS-INRIA-ENSTA UMR 2706 POEMS 32, Boulevard Victor, 75739 Paris Cedex 15, France;CNRS-INRIA-ENSTA UMR 2706 POEMS 32, Boulevard Victor, 75739 Paris Cedex 15, France;CNRS-INRIA-ENSTA UMR 2706 POEMS 32, Boulevard Victor, 75739 Paris Cedex 15, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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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.