Yee-like schemes on staggered cellular grids: A synthesis between FIT and FEM approaches

We propose an analysis (discretization techniques, convergence) of numerica l schemes for Maxwell equations which use two meshes (not necessarily tetra hedral), dual to each other. Schemes of this class generalize Yee's "finite difference in time domain" method (FDTD). We distinguish network equations (the discrete equivalents of Faraday's law and Ampere's relation), which c an be set up without any recourse to finite elements, and network constitut ive laws, whose validity cannot be assessed without them. This establishes a complementarity between "finite integration techniques" (FIT) and the fin ite element method (FEM). As an example, a Yee-like method on a simplicial mesh and its so-called "orthogonal" dual, is described, and its convergence is proved.