  This paper analyzes an abstract two-level algorithm for hybridizable
discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended
version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the
convergence rate of the algorithm, and show that the theoretical results also
apply to weak Galerkin (WG) methods. The main features of our analysis are
twofold: one is that we only need the minimal regularity of the model problem;
the other is that we do not require the triangulations to be quasi-uniform.
Numerical experiments are provided to confirm the theoretical results.
