  In this paper, we study a hybridizable discontinuous Galerkin (HDG) method
for the Maxwell operator. The only global unknowns are defined on the
inter-element boundaries, and the numerical solutions are obtained by using
discontinuous polynomial approximations. The error analysis is based on a mixed
curl-curl formulation for the Maxwell equations. Theoretical results are
obtained under a more general regularity requirement. In particular for the low
regularity case, special treatment is applied to approximate data on the
boundary. The HDG method is shown to be stable and convergence in an optimal
order for both high and low regularity cases. Numerical experiments with both
smooth and singular analytical solutions are performed to verify the
theoretical results.
