Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media
CoRR(2024)
摘要
This paper studies the family of interior penalty discontinuous Galerkin
methods for solving the Herrmann formulation of the linear elasticity
eigenvalue problem in heterogeneous media. By employing a weighted Lamé
coefficient norm within the framework of non-compact operators theory, we prove
convergence of both continuous and discrete eigenvalue problems as the mesh
size approaches zero, independently of the Lamé constants. Additionally, we
conduct an a posteriori analysis and propose a reliable and efficient
estimator. The theoretical findings are supported by numerical experiments.
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