The Hu-Zhang element for linear elasticity on curved domains
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916922640039936 |
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| author | Chen, Wei Du, Xinyuan Hu, Jun |
| author_facet | Chen, Wei Du, Xinyuan Hu, Jun |
| contents | This paper extends the Hu-Zhang element for linear elasticity to curved domains, preserving strong symmetry and H(div)-conformity. The non-polynomial structure of the curved Hu-Zhang element makes it difficult to analyze the stability, which is overcome by establishing a novel inf-sup condition. Optimal convergence rates are achieved for all variables except for the stress in the $L^2$-norm. This suboptimality originates from the fact that the divergence space of the curved Hu-Zhang element is not contained in the discrete displacement space, which is improved by local $p$-enrichment on boundary elements. Two numerical experiments validate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Hu-Zhang element for linear elasticity on curved domains Chen, Wei Du, Xinyuan Hu, Jun Numerical Analysis 65N12, 65N30, 74S05 This paper extends the Hu-Zhang element for linear elasticity to curved domains, preserving strong symmetry and H(div)-conformity. The non-polynomial structure of the curved Hu-Zhang element makes it difficult to analyze the stability, which is overcome by establishing a novel inf-sup condition. Optimal convergence rates are achieved for all variables except for the stress in the $L^2$-norm. This suboptimality originates from the fact that the divergence space of the curved Hu-Zhang element is not contained in the discrete displacement space, which is improved by local $p$-enrichment on boundary elements. Two numerical experiments validate the theoretical results. |
| title | The Hu-Zhang element for linear elasticity on curved domains |
| topic | Numerical Analysis 65N12, 65N30, 74S05 |
| url | https://arxiv.org/abs/2508.10674 |