In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the 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 general domain $\Omega$. Then, we establish the optimal order error estimates of the underlying HDG method with constant independent of the wavenumber. The theoretical results are confirmed by numerical experiments.

翻译：本文旨在针对三维空间中具有理想导体边界条件的不定时谐Maxwell方程，发展一种混合可间断Galerkin（HDG）方法。首先，我们推导了波数显式正则性结果，该结果在HDG方法的误差分析中起着重要作用。其次，我们证明了一个离散的inf-sup条件，该条件对所有正网格尺寸$h$、所有波数$k$以及一般区域$\Omega$均成立。随后，我们建立了该HDG方法的最优阶误差估计，其常数与波数无关。数值实验验证了理论结果。