Exact sequences on Powell–Sabin splits

  title={Exact sequences on Powell–Sabin splits},
  author={Johnny Guzm{\'a}n and Anna Lischke and Michael Neilan},
  journal={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. 

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