A $C^0$-continuous nonconforming virtual element method for linear strain gradient elasticity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915077015207936 |
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| author | Huang, Jianguo Yu, Yue |
| author_facet | Huang, Jianguo Yu, Yue |
| contents | A robust $C^0$-continuous nonconforming virtual element method (VEM) is developed for a boundary value problem arising from strain gradient elasticity in two dimensions, with the family of polygonal meshes satisfying a very general geometric assumption given in Brezzi et al. (2009) and Chen and Huang (2018). The stability condition of the VEMs is derived by establishing Korn-type inequalities and inverse inequalities. Some crucial commutative relations for locking-free analysis as in elastic problems are derived. The sharp and uniform error estimates with respect to both the microscopic parameter and the Lamé coefficient are achieved in the lowest-order case, which is also verified by numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A $C^0$-continuous nonconforming virtual element method for linear strain gradient elasticity Huang, Jianguo Yu, Yue Numerical Analysis 65N12, 65N15, 65N22, 65N30 A robust $C^0$-continuous nonconforming virtual element method (VEM) is developed for a boundary value problem arising from strain gradient elasticity in two dimensions, with the family of polygonal meshes satisfying a very general geometric assumption given in Brezzi et al. (2009) and Chen and Huang (2018). The stability condition of the VEMs is derived by establishing Korn-type inequalities and inverse inequalities. Some crucial commutative relations for locking-free analysis as in elastic problems are derived. The sharp and uniform error estimates with respect to both the microscopic parameter and the Lamé coefficient are achieved in the lowest-order case, which is also verified by numerical results. |
| title | A $C^0$-continuous nonconforming virtual element method for linear strain gradient elasticity |
| topic | Numerical Analysis 65N12, 65N15, 65N22, 65N30 |
| url | https://arxiv.org/abs/2412.17631 |