Mixed Finite element method for stress gradient elasticity
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911089761976320 |
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| author | Lin, Ting Tian, Shudan |
| author_facet | Lin, Ting Tian, Shudan |
| contents | This paper develops stable finite element pairs for the linear stress gradient elasticity model, overcoming classical elasticity's limitations in capturing size effects. We analyze mesh conditions to establish parameter-robust error estimates for the proposed pairs, achieving unconditional stability for finite elements with higher vertex continuity and conditional stability for Continuous Galerkin-Discontinuous Galerkin (CG-DG) pairs when no interior vertex has edges lying on three or fewer lines. Numerical experiments validate the theoretical results, demonstrating optimal convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed Finite element method for stress gradient elasticity Lin, Ting Tian, Shudan Numerical Analysis 65N30 This paper develops stable finite element pairs for the linear stress gradient elasticity model, overcoming classical elasticity's limitations in capturing size effects. We analyze mesh conditions to establish parameter-robust error estimates for the proposed pairs, achieving unconditional stability for finite elements with higher vertex continuity and conditional stability for Continuous Galerkin-Discontinuous Galerkin (CG-DG) pairs when no interior vertex has edges lying on three or fewer lines. Numerical experiments validate the theoretical results, demonstrating optimal convergence rates. |
| title | Mixed Finite element method for stress gradient elasticity |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2506.13041 |