  Recently, we proposed a weak Galerkin finite element method for the Laplace
eigenvalue problem. In this paper, we present two-grid and two-space skills to
accelerate the weak Galerkin method. By choosing parameters properly, the
two-grid and two-space weak Galerkin method not only doubles the convergence
rate, but also maintains the asymptotic lower bounds property of the weak
Galerkin method. Some numerical examples are provided to validate our
theoretical analysis.
