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A Construction of $C^{r}$ Conforming Finite Elements on the Alfeld Split in Any Dimension

Numerical Analysis 2026-04-06 v1 Numerical Analysis

Abstract

Constructing CrC^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.

Keywords

Cite

@article{arxiv.2604.03077,
  title  = {A Construction of $C^{r}$ Conforming Finite Elements on the Alfeld Split in Any Dimension},
  author = {Ting Lin and Hendrik Speleers and Qingyu Wu},
  journal= {arXiv preprint arXiv:2604.03077},
  year   = {2026}
}

Comments

34 pages, 5 figures