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01-06-2020

Exact sequences on Powell–Sabin splits

Authors: J. Guzmán, A. Lischke, M. Neilan

Published in: Calcolo | Issue 2/2020

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Abstract

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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Title: Exact sequences on Powell–Sabin splits
Authors: J. Guzmán
A. Lischke
M. Neilan
Publication date: 01-06-2020
Publisher: Springer International Publishing
Published in: Calcolo / Issue 2/2020
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-020-00361-x

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