The lower bound property of the Morley element eigenvalues

2015/09/02 by Yidu Yang, Hao Li, Yang, Yidu +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1509.00566

openalex publication_date 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that the Morley element eigenvalues approximate the exact ones from below on regular meshes, including adaptive local refined meshes, for the fourth-order elliptic eigenvalue problems with the clamped boundary condition in any dimension. And we implement the adaptive computation to obtain lower bounds of the Morley element eigenvalues for the vibration problem of clamped plate under tension.

Related

• Upper and lower bounds for eigenvalues of the clamped plate problem
• A lower bound for eigenvalues of a clamped plate problem
• New Fourth Order Postprocessing Techniques for Plate Bending Eigenvalues by Morley Element
• Morley Finite Element Method for the Eigenvalues of the Biharmonic\n Operator
• Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem