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

• Published in: Journal of computational and applied mathematics Vol. 204; no. 2; pp. 408 - 417
• Main Authors: Bonnet-Ben Dhia, A.S., Ciarlet Jr, P., Zwölf, C.M.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 15.07.2007; Elsevier
• Subjects: Augmented variational formulation; Exact sciences and technology; Mathematical analysis; Mathematics; Numerical Analysis; Numerical analysis. Scientific computation; Opposite sign dielectric constants; Partial differential equations; Sciences and techniques of general use; Wave transmission problem; Wave transmission problem; Opposite sign dielectric constants; Augmented variational formulation; Wave equation; Finite element method; Transmission problem; Numerical analysis; Applied mathematics; Numerical method; Augmented varialional formulation; Maxwell equation; Implementation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2006.01.046

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.