A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations

In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for solving the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary condition in three-dimensional space. First, we derive a wavenumber explicit regularity result, which plays an important role in the error analysis for the HDG method. Second, we prove a discrete inf-sup condition which holds for all positive mesh size h, for all wavenumber k, and for the general domain. Then, we establish optimal order error estimates of the proposed HDG method with constants being explicitly dependent on the wavenumber. The theoretical results are confirmed by numerical experiments.