A DG method for a stress formulation of the elasticity eigenproblem with strongly imposed symmetry
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Publication:6398346
DOI10.1016/J.CAMWA.2023.01.022arXiv2205.02707MaRDI QIDQ6398346
Publication date: 5 May 2022
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 demonstrate 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.
Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)
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