Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media
<|reference_start|>Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media: 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.<|reference_end|>
@article{khan2024interior,
    title={Interior penalty discontinuous Galerkin methods for the nearly
  incompressible elasticity eigenvalue problem with heterogeneous media},
    author={Arbaz Khan and Felipe Lepe and Jesus Vellojin},
    journal={arXiv preprint arXiv:2402.17711},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17711},
    primaryClass={math.NA cs.NA}
}