A Construction of $C^{r}$ Conforming Finite Elements on the Alfeld Split in Any Dimension
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914443222319104 |
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| author | Lin, Ting Speleers, Hendrik Wu, Qingyu |
| author_facet | Lin, Ting Speleers, Hendrik Wu, Qingyu |
| contents | Constructing $C^r$ conforming finite element spaces in any dimension is a long-standing problem. For general triangulations, this problem was recently addressed by Hu-Lin-Wu (2024), under certain conditions on supersmoothness and polynomial degree. In this paper, a first unified construction on the Alfeld split in any dimension is given, where the supersmoothness conditions and the polynomial degree requirement are relaxed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03077 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Construction of $C^{r}$ Conforming Finite Elements on the Alfeld Split in Any Dimension Lin, Ting Speleers, Hendrik Wu, Qingyu Numerical Analysis 65N30, 65D07, 41A15 Constructing $C^r$ conforming finite element spaces in any dimension is a long-standing problem. For general triangulations, this problem was recently addressed by Hu-Lin-Wu (2024), under certain conditions on supersmoothness and polynomial degree. In this paper, a first unified construction on the Alfeld split in any dimension is given, where the supersmoothness conditions and the polynomial degree requirement are relaxed. |
| title | A Construction of $C^{r}$ Conforming Finite Elements on the Alfeld Split in Any Dimension |
| topic | Numerical Analysis 65N30, 65D07, 41A15 |
| url | https://arxiv.org/abs/2604.03077 |