Robust and Optimal Mixed Methods for a Fourth-Order Elliptic Singular Perturbation Problem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912590337146880 |
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| author | Huang, Xuehai Tang, Zheqian |
| author_facet | Huang, Xuehai Tang, Zheqian |
| contents | A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed method based on a second-order system is proposed without relying on Nitsche's technique or interpolations. Robust and optimal error estimates are derived using an $L^2$-bounded interpolation operator for tensors. Then, its connections to other discrete methods, including weak Galerkin methods and a mixed finite element method based on a first-order system, are established. Finally, numerical experiments are provided to validate the theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_12137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust and Optimal Mixed Methods for a Fourth-Order Elliptic Singular Perturbation Problem Huang, Xuehai Tang, Zheqian Numerical Analysis 65N12, 65N22, 65N30 A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed method based on a second-order system is proposed without relying on Nitsche's technique or interpolations. Robust and optimal error estimates are derived using an $L^2$-bounded interpolation operator for tensors. Then, its connections to other discrete methods, including weak Galerkin methods and a mixed finite element method based on a first-order system, are established. Finally, numerical experiments are provided to validate the theoretical results. |
| title | Robust and Optimal Mixed Methods for a Fourth-Order Elliptic Singular Perturbation Problem |
| topic | Numerical Analysis 65N12, 65N22, 65N30 |
| url | https://arxiv.org/abs/2501.12137 |