An adaptive multilevel method for time-harmonic maxwell equations with singularities, preprint

Abstract. We develop an adaptive edge finite element method based on reliable and efficient residual-based a posteriori error estimates for low-frequency time-harmonic Maxwell’s equations with singularities. The resulting discrete problem is solved by the multigrid preconditioned minimum residual iteration algorithm. We demonstrate the efficiency and robustness of the proposed method by extensive numerical experiments for cavity problems with singular solutions which includes, in particular, scattering over screens. Key words. Maxwell’s equations, singularities of solutions, adaptive finite element method, multigrid method AMS subject classifications. 65N30, 65N55, 78A2