Heterogeneous multiscale method for Maxwell’s equations

We present a Finite Element Heterogeneous Multiscale Method (FE-HMM) for time-dependent Maxwell’s equations in first-order formulation in highly oscillatory materials using Nédélec’s edge elements. Based on a uniform approach for the error analysis of non-conforming space discretizations, we prove an error bound for the semidiscrete scheme. We further present error bounds for the fully discrete scheme, where we consider time discretization using algebraically stable Runge-Kutta methods, the Crank-Nicolson method and the leapfrog method. These error bounds are confirmed by numerical experiments.