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

2007
Publication type:
Paper in peer-reviewed journals
Journal:
Journal of Computational and Applied Mathematics, vol. 204 (2 SPEC), pp. 408-417
HAL:
Abstract:
We consider a simplified scalar model problem related to Maxwell equations, involving wave transmission between media with opposite sign dielectric constant. We build two variational formulations equivalent to model problem. We show that, under some suitable conditions, every formulation is well posed since it fits 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 $L^\infty$ dielectric constant. Moreover the three-field formulation allows to handle a more general set of equations. A main interest of these formulations is that they allow a simple finite element numerical treatement.
BibTeX:
@article{Bon-Cia-Zwo-2007,
author={Anne-Sophie Bonnet-BenDhia and Patrick Ciarlet and Carlo Maria
Zwölf },
title={Two-field and three-field formulations for wave transmission
between media with opposite sign dielectric constants },
doi={10.1016/j.cam.2006.01.046 },
journal={Journal of Computational and Applied Mathematics },
year={2007 },
volume={204 (2 SPEC) },
pages={408--417},
}