The two-grid weak Galerkin method and enriched Crouzeix-Raviart element method for linear elastic eigenvalue problems

TL;DR

This paper introduces a two-grid weak Galerkin method that accelerates convergence and preserves lower bounds, along with an enriched Crouzeix-Raviart scheme for linear elastic eigenvalue problems, enhancing computational efficiency and accuracy.

Contribution

The paper proposes a novel two-grid weak Galerkin method and an enriched Crouzeix-Raviart scheme, both providing lower bounds and improved convergence for linear elastic eigenvalue problems.

Findings

Two-grid weak Galerkin method doubles convergence rate.

Method maintains asymptotic lower bounds property.

Enriched Crouzeix-Raviart scheme provides lower bounds for eigenvalues.

Abstract

In this paper, we present a two-gird skill to accelerate the weak Galerkin method. By the proper use of parameters, the two-grid weak Galerkin method not only doubles the convergence rate, but also maintains the asymptotic lower bounds property of the weak Galerkin (WG) method. Moreover, we propose an enriched Crouzeix-Raviart (ECR) scheme, which can also provide lower bounds for the linear elastic eigenvalue problems.