A Coupling Method of Mixed and Lagrange Finite Elements for Linear Elasticity Problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866917420951666688 |
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| author | Chen, Wei Hu, Jun Ma, Limin Zhang, Mingyan |
| author_facet | Chen, Wei Hu, Jun Ma, Limin Zhang, Mingyan |
| contents | This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress concentration, while standard Lagrange elements are used elsewhere, achieving a balance between stress accuracy and computational efficiency. The well-posedness of the coupled formulation and optimal a priori error estimates are established, even when the size of the mixed finite element subregion is $O(h)$. Numerical experiments are presented to verify the theoretical convergence rates and to demonstrate the effectiveness and efficiency of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17908 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Coupling Method of Mixed and Lagrange Finite Elements for Linear Elasticity Problem Chen, Wei Hu, Jun Ma, Limin Zhang, Mingyan Numerical Analysis This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress concentration, while standard Lagrange elements are used elsewhere, achieving a balance between stress accuracy and computational efficiency. The well-posedness of the coupled formulation and optimal a priori error estimates are established, even when the size of the mixed finite element subregion is $O(h)$. Numerical experiments are presented to verify the theoretical convergence rates and to demonstrate the effectiveness and efficiency of the proposed method. |
| title | A Coupling Method of Mixed and Lagrange Finite Elements for Linear Elasticity Problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.17908 |