Stabilized interior penalty methods for the time-harmonic Maxwell equations

We propose stabilized interior penalty discontinuous Galerkin methods for the indefinite time–harmonic Maxwell system. The methods are based on a mixed formulation of the boundary value problem chosen to provide control on the divergence of the electric field. We prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach. Key words: Finite elements, discontinuous Galerkin methods, interior penalty methods, time-harmonic Maxwell’s equations