The Weak Galerkin and Crouzeix-Raviart element method for elastic eigenvalue problems

2025/08/04 by Wei Lu, Lu, Wei, Xie, Hehu +2
Computer Science · Engineering · #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #Eigenvalues and eigenvectors #Element (criminal law) #FOS: Mathematics #Finite element method #Galerkin method #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical analysis #Upper and lower bounds

paper · pdf · doi:10.48550/arxiv.2508.02064

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we first introduce an abstract framework to solve the eigenvalue problem by weak Galerkin (WG) method. By the application of the framework, WG method is proved to be locking-free and gives asymptotic lower bounds for the elastic eigenvalue problem. Also, we analyze the lower bound property for Crouzeix-Raviart (CR) element as an extensional work. In the end, we present some numerical experiments to support the theoretical results.

Citations

• A virtual element method for the elasticity spectral problem allowing small edges
• A posteriori analysis for a mixed FEM discretization of the linear elasticity spectral problem
• The nonconforming Crouzeix-Raviart element approximation and two-grid discretizations for the elastic eigenvalue problem
• Displacement-pseudostress formulation for the linear elasticity spectral problem
• Mixed discontinuous Galerkin approximation of the elasticity\n eigenproblem
• A Locking-Free Weak Galerkin Finite Element Method for Elasticity Problems in the Primal Formulation
• Weak Galerkin method for the coupled Darcy-Stokes flow
• An Efficient Numerical Scheme for the Biharmonic Equation by Weak Galerkin Finite Element Methods on Polygonal or Polyhedral Meshes
• A Weak Galerkin Finite Element Method with Polynomial Reduction
• Verified eigenvalue evaluation for Laplacian over polygonal domain of arbitrary shape

Related

• The two-grid weak Galerkin method and enriched Crouzeix-Raviart element method for linear elastic eigenvalue problems
• The nonconforming Crouzeix-Raviart element approximation and two-grid discretizations for the elastic eigenvalue problem
• The weak Galerkin method for eigenvalue problems
• Computing Both Upper and Lower Eigenvalue Bounds by HDG Methods
• The weak Galerkin finite element method for the Steklov eigenvalue problem