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 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