A novel parameter-free and locking-free enriched Galerkin method for linear elasticity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915301587681280 |
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| author | Su, Shuai Yan, Xiurong Zhang, Qian |
| author_facet | Su, Shuai Yan, Xiurong Zhang, Qian |
| contents | We propose a novel parameter-free and locking-free enriched Galerkin (EG) method for solving the linear elasticity problem in both two and three dimensions. Unlike existing locking-free EG methods, our method enriches the first-order continuous Galerkin (CG) space with piecewise constants along edges in two dimensions or faces in three dimensions. This enrichment acts as a correction to the normal component of the CG space, ensuring the locking-free property and delivering an oscillation-free stress approximation without requiring post-processing. Our theoretical analysis establishes the well-posedness of the method and derives optimal error estimates. Numerical experiments further demonstrate the accuracy, efficiency, and robustness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A novel parameter-free and locking-free enriched Galerkin method for linear elasticity Su, Shuai Yan, Xiurong Zhang, Qian Numerical Analysis 65N30 and 65N15 and 65N12 and 35B45 and 78M10 We propose a novel parameter-free and locking-free enriched Galerkin (EG) method for solving the linear elasticity problem in both two and three dimensions. Unlike existing locking-free EG methods, our method enriches the first-order continuous Galerkin (CG) space with piecewise constants along edges in two dimensions or faces in three dimensions. This enrichment acts as a correction to the normal component of the CG space, ensuring the locking-free property and delivering an oscillation-free stress approximation without requiring post-processing. Our theoretical analysis establishes the well-posedness of the method and derives optimal error estimates. Numerical experiments further demonstrate the accuracy, efficiency, and robustness of the proposed method. |
| title | A novel parameter-free and locking-free enriched Galerkin method for linear elasticity |
| topic | Numerical Analysis 65N30 and 65N15 and 65N12 and 35B45 and 78M10 |
| url | https://arxiv.org/abs/2505.18042 |