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arXiv · 2402.17711

Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media

Arbaz Khan·Felipe Lepe·Jesus Vellojin
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Abstract

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 Lam\'e 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 Lam\'e 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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Arbaz Khan, Felipe Lepe, Jesus Vellojin. 2024-02-27. Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media. https://arxiv.org/abs/2402.17711

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