Exact sequences on Worsey–Farin splits

Guzmán, Johnny; Lischke, Anna; Neilan, Michael

doi:10.1090/mcom/3746

Exact sequences on Worsey–Farin splits
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by Johnny Guzmán, Anna Lischke and Michael Neilan;

Math. Comp. 91 (2022), 2571-2608

DOI: https://doi.org/10.1090/mcom/3746

Published electronically: July 12, 2022

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Abstract:

We construct several smooth finite element spaces defined on three-dimensional Worsey–Farin splits. In particular, we construct $C^1$, $H^1(\operatorname {curl})$, and $H^1$-conforming finite element spaces and show the discrete spaces satisfy local exactness properties. A feature of the spaces is their low polynomial degree and lack of extrinsic supersmoothness at subsimplices of the mesh. In the lowest order case, the last two spaces in the sequence consist of piecewise linear and piecewise constant spaces, and are suitable for the discretization of the (Navier-)Stokes equation.

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