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

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)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.