The interior penalty virtual element method for the two-dimensional biharmonic eigenvalue problem

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Jian Meng
  • Bing Bing Xu
  • Fang Su
  • Xu Qian

Research Organisations

External Research Organisations

  • National University of Defense Technology
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Details

Original languageEnglish
Article number117685
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Volume436
Early online date28 Dec 2024
Publication statusE-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

Cite this

The interior penalty virtual element method for the two-dimensional biharmonic eigenvalue problem. / Meng, Jian; Xu, Bing Bing; Su, Fang et al.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 436, 117685, 01.03.2025.

Research output: Contribution to journalArticleResearchpeer review

Meng J, Xu BB, Su F, Qian X. The interior penalty virtual element method for the two-dimensional biharmonic eigenvalue problem. Computer Methods in Applied Mechanics and Engineering. 2025 Mar 1;436:117685. Epub 2024 Dec 28. doi: 10.1016/j.cma.2024.117685
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