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

A two-level algorithm for the weak Galerkin discretization of diffusion problems