Acceleration of weak Galerkin methods for the Laplacian eigenvalue problem

TL;DR

This paper introduces two-grid and two-space techniques to accelerate the weak Galerkin finite element method for the Laplacian eigenvalue problem, effectively doubling convergence rates while preserving key properties.

Contribution

The paper develops and analyzes two-grid and two-space acceleration strategies for the weak Galerkin method, enhancing efficiency without losing accuracy.

Findings

Doubling of convergence rate with proper parameter selection

Preservation of asymptotic lower bounds property

Numerical validation confirms theoretical results

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.