The Weak Galerkin and Crouzeix-Raviart element method for elastic eigenvalue problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911090097520640 |
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| author | Lu, Wei Xie, Hehu Zhai, Qilong |
| author_facet | Lu, Wei Xie, Hehu Zhai, Qilong |
| contents | In this paper, we first introduce an abstract framework to solve the eigenvalue problem by weak Galerkin (WG) method. By the application of the framework, WG method is proved to be locking-free and gives asymptotic lower bounds for the elastic eigenvalue problem. Also, we analyze the lower bound property for Crouzeix-Raviart (CR) element as an extensional work. In the end, we present some numerical experiments to support the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Weak Galerkin and Crouzeix-Raviart element method for elastic eigenvalue problems Lu, Wei Xie, Hehu Zhai, Qilong Numerical Analysis In this paper, we first introduce an abstract framework to solve the eigenvalue problem by weak Galerkin (WG) method. By the application of the framework, WG method is proved to be locking-free and gives asymptotic lower bounds for the elastic eigenvalue problem. Also, we analyze the lower bound property for Crouzeix-Raviart (CR) element as an extensional work. In the end, we present some numerical experiments to support the theoretical results. |
| title | The Weak Galerkin and Crouzeix-Raviart element method for elastic eigenvalue problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.02064 |