Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems. (1st September 2022)

• Record Type: Journal Article
• Authors: Dassi, Franco; Velásquez, Iván
• Is Part Of: Computers & mathematics with applications. Volume 121(2022)
• Page Start: 85
• Page End: 101
• Publication Date: 2022-09-01
• Subjects: Bi-harmonic eigenvalue problems -- Virtual element method -- Polyhedral meshes -- Error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.07.001
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper we study a C 1 Virtual Element Method (VEM) on polyhedral meshes for bi-harmonic eigenvalue problems in three dimensions. Optimal order error estimates for the eigenfunctions and a double order for the eigenvalues are obtained by using the approximation theory of compact self-adjoint operators. Finally, a set of tests will numerically prove the theoretical result of the proposed scheme.