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

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 $L^2$ norm least squares functional with the weak imposition of the continuity across the 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 convergence orders under both the energy norm and the $L^2$ norm. Numerical results in two and three dimensions are presented to verify the error estimates.