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We present and analyze a hybridizable discontinuous Galerkin (HDG) method forthe time-harmonic Maxwell equations. The divergence-free condition is enforcedon the electric field, then a Lagrange multiplier is introduced, and theproblem becomes the solution of a mixed curl-curl formulation of the Maxwell'sproblem. The method is shown to be an absolutely stable HDG method for theindefinite time-harmonic Maxwell equations with high wave number. By exploitingthe duality argument, the dependence of convergence of the HDG method on thewave number k, the mesh size h and the polynomial order p is obtained.Numerical results are given to verify the theoretical analysis.

An absolutely stable $hp$-HDG method for the time-harmonic Maxwell equations with high wave number