Acceleration of weak Galerkin methods for the Laplacian eigenvalue problem

2017/08/28 by Qilong Zhai, Hehu Xie, Zhai, Qilong +5
Computer Science · Engineering · #35B45 #35J35 #35J50 #65N12 #65N15 #65N30 #74N20 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Primary #Secondary

paper · pdf · doi:10.48550/arxiv.1708.08183

openalex publication_date 2017/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Related

• The weak Galerkin method for eigenvalue problems
• The two-grid weak Galerkin method and enriched Crouzeix-Raviart element method for linear elastic eigenvalue problems
• Augmented Subspace Scheme for Eigenvalue Problem by Weak Galerkin Finite Element Method
• A weak Galerkin finite element method for solving the asymptotic lower bound of Maxwell eigenvalue problem
• The weak Galerkin finite element method for the Steklov eigenvalue problem