  This paper analyzes a two-level algorithm for the weak Galerkin (WG) finite
element methods based on local Raviart-Thomas (RT) and Brezzi-Douglas-Marini
(BDM) mixed elements for two- and three-dimensional diffusion problems with
Dirichlet condition. We first show the condition numbers of the stiffness
matrices arising from the WG methods are of $O(h^{-2})$. We use an extended
version of the Xu-Zikatanov (XZ) identity to derive the convergence of the
algorithm without any regularity assumption. Finally we provide some numerical
results.
