Polynomial preserving recovery for PHT-splines
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911106098790400 |
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| author | Cai, Ying Chen, Falai Guo, Hailong Kang, Hongmei Zhang, Zhimin |
| author_facet | Cai, Ying Chen, Falai Guo, Hailong Kang, Hongmei Zhang, Zhimin |
| contents | We propose a polynomial preserving recovery method for PHT-splines within isogeometric analysis to obtain more accurate gradient approximations. The method fully exploits the local interpolation properties of PHT-splines and avoids the need for information on gradient superconvergent points. By leveraging the superconvergence argument of difference quotients and the interior error estimate, we establish the superconvergence property of the recovered gradient on translation invariant meshes. As a byproduct, a recovery-based a posteriori error estimator is developed for adaptive refinement. Numerical results confirm the theoretical findings and demonstrate the effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial preserving recovery for PHT-splines Cai, Ying Chen, Falai Guo, Hailong Kang, Hongmei Zhang, Zhimin Numerical Analysis We propose a polynomial preserving recovery method for PHT-splines within isogeometric analysis to obtain more accurate gradient approximations. The method fully exploits the local interpolation properties of PHT-splines and avoids the need for information on gradient superconvergent points. By leveraging the superconvergence argument of difference quotients and the interior error estimate, we establish the superconvergence property of the recovered gradient on translation invariant meshes. As a byproduct, a recovery-based a posteriori error estimator is developed for adaptive refinement. Numerical results confirm the theoretical findings and demonstrate the effectiveness of the proposed method. |
| title | Polynomial preserving recovery for PHT-splines |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.11233 |