Convergence Analysis of a Finite Volume Method for Maxwell's Equations in Nonhomogeneous Media

In this paper, we analyze a recently developed finite volume method for the timedependent Maxwell’s equations in a three-dimensional polyhedral domain composed of two dielectric materials with different parameter values for the electric permittivity and the magnetic permeability. Convergence and error estimates of the numerical scheme are established for general nonuniform tetrahedral triangulations of the physical domain. In the case of nonuniform rectangular grids, the scheme converges with second order accuracy in the discrete L2-norm, despite the low regularity of the true solution over the entire domain. In particular, the finite volume method is shown to be superconvergent in the discrete H(curl; Ω)-norm. In addition, the explicit dependence of the error estimates on the material parameters is given.