A discontinuous least squares finite element method for time-harmonic Maxwell equations

Abstract

We propose and analyze a discontinuous least squares finite element method for solving the indefinite time-harmonic Maxwell equations. The scheme is based on the L2 norm least squares functional with weak imposition of continuity across interior faces. We minimize the functional over the piecewise polynomial spaces to seek numerical solutions. The method is shown to be stable without any constraint on the mesh size. We prove the optimal convergence rate under the energy norm and sub-optimal convergence rate under the L2 norm. Numerical results in two and three dimensions are presented to verify the error estimates.