Details
Original language | English |
---|---|
Article number | 117685 |
Number of pages | 20 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 436 |
Early online date | 28 Dec 2024 |
Publication status | E-pub ahead of print - 28 Dec 2024 |
Abstract
The biharmonic eigenvalue problem is a fourth order eigenmodel appearing in many applications of the mechanics, fluid and inverse scattering theory. In this paper, we introduce the interior penalty virtual element method for the biharmonic eigenvalue problem in two dimensions. It preserves the symmetric positive-definiteness of the continuous problem and reduces the total number of required degrees of freedom. Considering standard assumptions on polygonal meshes, we prove the correct approximation of spectrum for the proposed virtual element scheme. Necessitated by supporting the convergence analysis, representative numerical examples are reported, including the optimal convergence on different meshes, the associate vibration and buckling problems with clamped, simply supported and Cahn–Hilliard boundary conditions, together with developing Serendipity version dropping the internal-to-element degrees of freedom.
Keywords
- Biharmonic eigenvalue problem, Error estimates, Interior penalty VEM, Spectral approximation, The vibration and buckling problems of Kirchhoff–Love plate
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 436, 117685, 01.03.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The interior penalty virtual element method for the two-dimensional biharmonic eigenvalue problem
AU - Meng, Jian
AU - Xu, Bing Bing
AU - Su, Fang
AU - Qian, Xu
N1 - Publisher Copyright: © 2024 Elsevier B.V.
PY - 2024/12/28
Y1 - 2024/12/28
N2 - The biharmonic eigenvalue problem is a fourth order eigenmodel appearing in many applications of the mechanics, fluid and inverse scattering theory. In this paper, we introduce the interior penalty virtual element method for the biharmonic eigenvalue problem in two dimensions. It preserves the symmetric positive-definiteness of the continuous problem and reduces the total number of required degrees of freedom. Considering standard assumptions on polygonal meshes, we prove the correct approximation of spectrum for the proposed virtual element scheme. Necessitated by supporting the convergence analysis, representative numerical examples are reported, including the optimal convergence on different meshes, the associate vibration and buckling problems with clamped, simply supported and Cahn–Hilliard boundary conditions, together with developing Serendipity version dropping the internal-to-element degrees of freedom.
AB - The biharmonic eigenvalue problem is a fourth order eigenmodel appearing in many applications of the mechanics, fluid and inverse scattering theory. In this paper, we introduce the interior penalty virtual element method for the biharmonic eigenvalue problem in two dimensions. It preserves the symmetric positive-definiteness of the continuous problem and reduces the total number of required degrees of freedom. Considering standard assumptions on polygonal meshes, we prove the correct approximation of spectrum for the proposed virtual element scheme. Necessitated by supporting the convergence analysis, representative numerical examples are reported, including the optimal convergence on different meshes, the associate vibration and buckling problems with clamped, simply supported and Cahn–Hilliard boundary conditions, together with developing Serendipity version dropping the internal-to-element degrees of freedom.
KW - Biharmonic eigenvalue problem
KW - Error estimates
KW - Interior penalty VEM
KW - Spectral approximation
KW - The vibration and buckling problems of Kirchhoff–Love plate
UR - http://www.scopus.com/inward/record.url?scp=85213277753&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.117685
DO - 10.1016/j.cma.2024.117685
M3 - Article
AN - SCOPUS:85213277753
VL - 436
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 117685
ER -