A DG method for a stress formulation of the elasticity eigenproblem with strongly imposed symmetry

2022/05/05 by Salim Meddahi, Meddahi, Salim · 3 citations
Engineering · #65N12 #65N15 #65N30 #74B10 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2205.02707

openalex publication_date 2022/05/05 · openalex created_date 2022/05/08 · openalex updated_date 2026/07/28

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.

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