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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.04805 |
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| _version_ | 1866917463893999616 |
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| author | Zhou, Yihui Li, Yuwen |
| author_facet | Zhou, Yihui Li, Yuwen |
| contents | This work derives a posteriori error estimate of polygonal finite element methods based on Wachspress barycentric coordinates. In particular, we prove that the classical residual-based a posteriori error estimator is both an upper and lower bounds for the discretization error. The analysis relies a Scott-Zhang type interpolation and homogeneity arguments for rational functions on polygonal elements. Numerical experiments on square and L-shaped domains demonstrate the effectiveness of the adaptive algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04805 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Adaptive Finite Element Method Based on Generalized Barycentric Coordinates Zhou, Yihui Li, Yuwen Numerical Analysis This work derives a posteriori error estimate of polygonal finite element methods based on Wachspress barycentric coordinates. In particular, we prove that the classical residual-based a posteriori error estimator is both an upper and lower bounds for the discretization error. The analysis relies a Scott-Zhang type interpolation and homogeneity arguments for rational functions on polygonal elements. Numerical experiments on square and L-shaped domains demonstrate the effectiveness of the adaptive algorithm. |
| title | An Adaptive Finite Element Method Based on Generalized Barycentric Coordinates |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.04805 |