  We consider the numerical approximation of the spectrum of a second-order
elliptic eigenvalue problem by the hybridizable discontinuous Galerkin (HDG)
method. We show for problems with smooth eigenfunctions that the approximate
eigenvalues and eigenfunctions converge at the rate 2k+1 and k+1, respectively.
Here k is the degree of the polynomials used to approximate the solution, its
flux, and the numerical traces. Our numerical studies show that a Rayleigh
quotient-like formula applied to certain locally postprocessed approximations
can yield eigenvalues that converge faster at the rate 2k + 2 for the HDG
method as well as for the Brezzi-Douglas-Marini (BDM) method. We also derive
and study a condensed nonlinear eigenproblem for the numerical traces obtained
by eliminating all the other variables.
