A DG method for a stress formulation of the elasticity eigenproblem with strongly imposed symmetry. (1st April 2023)

• Record Type: Journal Article
• Authors: Meddahi, Salim
• Is Part Of: Computers & mathematics with applications. Volume 135(2023)
• Page Start: 19
• Page End: 30
• Publication Date: 2023-04-01
• Subjects: Elasticity eigenproblem -- Mixed DG methods -- Spectral analysis -- Error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2023.01.022
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We introduce a pure–stress formulation of the elasticity eigenvalue problem with mixed boundary conditions. We propose an H(div)-based discontinuous Galerkin method that imposes strongly the symmetry of the stress for the discretization of the eigenproblem. Under appropriate assumptions on the mesh and the degree of polynomial approximation, we prove the spectral correctness of the discrete scheme and derive optimal rates of convergence for eigenvalues and eigenfunctions. Finally, we provide numerical examples in two and three dimensions.