Numerical approximation of the maxwell equations in inhomogeneous media by a P¹ conforming finite element method

The aim of this paper is to present an extension of the P¹ conforming finite element method for the time-dependent Maxwell equations that has been previously exposed. We shall consider inhomogeneous media with the piecewise constant dielectric and magnetic parameters, and precisely, the interface of two such media. By analogy with the idea developed, we propose a method based on the dualization and then the approximation of the interface conditions in a way consistent with the one derived for the fields and the Lagrange multipliers of the divergence constraints inside the domain.