# Exact sequences on Powell–Sabin splits

@article{Guzmn2019ExactSO,
title={Exact sequences on Powell–Sabin splits},
author={Johnny Guzm{\'a}n and Anna Lischke and Michael Neilan},
journal={arXiv: Numerical Analysis},
year={2019}
}
• Published 2019
• Mathematics
• arXiv: Numerical Analysis
We construct smooth finite elements spaces on Powell-Sabin triangulations that form an exact sequence. The first space of the sequence coincides with the classical $C^1$ Powell-Sabin space, while the others form stable and divergence-free yielding pairs for the Stokes problem. We develop degrees of freedom for these spaces that induce projections that commute with the differential operators.
6 Citations

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