  We present the hybridization of flux reconstruction methods for
advection-diffusion problems. Hybridization introduces a new variable into the
problem so that it can be reduced via static condensation. This allows the
solution of implicit discretizations to be done more efficiently. We derive an
energy statement from a stability analysis considering a range of correction
functions on hybridized and embedded flux reconstruction schemes. Then, we
establish connections to standard formulations. We devise a post-processing
scheme that leverages existing flux reconstruction operators to enhance
accuracy for diffusion-dominated problems. Results show that the implicit
convergence of these methods for advection-diffusion problems can result in
performance benefits of over an order of magnitude. In addition, we observe
that the superconvergence property of hybridized methods can be extended to the
family of FR schemes for a range of correction functions.
