Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910345722855424 |
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| author | Khan, Arbaz Lepe, Felipe Vellojin, Jesus |
| author_facet | Khan, Arbaz Lepe, Felipe Vellojin, Jesus |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_17711 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media Khan, Arbaz Lepe, Felipe Vellojin, Jesus Numerical Analysis 35Q35, 65N15, 65N25, 65N30, 76D07 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. |
| title | Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media |
| topic | Numerical Analysis 35Q35, 65N15, 65N25, 65N30, 76D07 |
| url | https://arxiv.org/abs/2402.17711 |