A linear virtual element method for the Kirchhoff plate buckling problem. (May 2020)

• Record Type: Journal Article
• Authors: Meng, Jian; Mei, Liquan
• Is Part Of: Applied mathematics letters. Volume 103(2020)
• Publication Date: 2020-05
• Subjects: Linear virtual element method -- Polygonal meshes -- Buckling problem -- Spectral approximation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106188
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, a linear virtual element method for the approximation of the Kirchhoff plate buckling eigenvalue problem subjected to the simply supported boundary condition is studied. We give the weak formulation of the spectral problem by introducing an auxiliary variable, and construct a piecewise linear and lower regular virtual element space. Moreover, we employ the spectral theory of compact operator to prove the spectral approximation and optimal order for the eigenvalues. Finally, some numerical results are presented.