Acceleration of weak Galerkin methods for the Laplacian eigenvalue problem
For researchers in numerical methods for eigenvalue problems, this work offers an acceleration technique that improves efficiency without sacrificing accuracy.
The authors accelerate weak Galerkin methods for the Laplacian eigenvalue problem using two-grid and two-space techniques, achieving double the convergence rate while preserving asymptotic lower bounds.
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.