A Construction of $C^{r}$ Conforming Finite Elements on the Alfeld Split in Any Dimension
Ting Lin, Hendrik Speleers, Qingyu Wu
TL;DR
This paper presents a unified method for constructing $C^r$ conforming finite element spaces on the Alfeld split in any dimension, relaxing previous supersmoothness and polynomial degree constraints.
Contribution
It introduces a new unified construction that overcomes earlier limitations on supersmoothness and polynomial degree for finite elements on the Alfeld split.
Findings
Provides a construction applicable in any dimension
Relaxes supersmoothness conditions
Reduces polynomial degree requirements
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.
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