Optimality of adaptive $H(\operatorname{div}\operatorname{div})$ mixed finite element methods for the Kirchhoff-Love plate bending problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918123914919936 |
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| author | Hu, Jun Ma, Rui Zhang, Min |
| author_facet | Hu, Jun Ma, Rui Zhang, Min |
| contents | This paper presents a reliable and efficient residual-based a posteriori error analysis for the symmetric $H(\operatorname{div}\operatorname{div})$ mixed finite element method for the Kirchhoff-Love plate bending problem with mixed boundary conditions. The key ingredient lies in the construction of boundary-condition-preserving complexes at both continuous and discrete levels. Additionally, the discrete symmetric $H(\operatorname{div}\operatorname{div})$ space is extended to ensure nestedness, which leads to optimality for the adaptive algorithm. Numerical examples confirm the effectiveness of the a posteriori error estimator and demonstrate the optimal convergence rate under adaptive refinements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimality of adaptive $H(\operatorname{div}\operatorname{div})$ mixed finite element methods for the Kirchhoff-Love plate bending problem Hu, Jun Ma, Rui Zhang, Min Numerical Analysis Primary 65N30, 65N15, 65N50 This paper presents a reliable and efficient residual-based a posteriori error analysis for the symmetric $H(\operatorname{div}\operatorname{div})$ mixed finite element method for the Kirchhoff-Love plate bending problem with mixed boundary conditions. The key ingredient lies in the construction of boundary-condition-preserving complexes at both continuous and discrete levels. Additionally, the discrete symmetric $H(\operatorname{div}\operatorname{div})$ space is extended to ensure nestedness, which leads to optimality for the adaptive algorithm. Numerical examples confirm the effectiveness of the a posteriori error estimator and demonstrate the optimal convergence rate under adaptive refinements. |
| title | Optimality of adaptive $H(\operatorname{div}\operatorname{div})$ mixed finite element methods for the Kirchhoff-Love plate bending problem |
| topic | Numerical Analysis Primary 65N30, 65N15, 65N50 |
| url | https://arxiv.org/abs/2508.09008 |