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arXiv · 2008.06429

Divergence--free Scott--Vogelius elements on curved domains

Michael Neilan·M. Baris Otus
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Abstract

We construct and analyze an isoparametric finite element pair for the Stokes problem in two dimensions. The pair is defined by mapping the Scott-Vogelius finite element space via a Piola transform. The velocity space has the same degrees of freedom as the quadratic Lagrange finite element space, and therefore the proposed spaces reduce to the Scott-Vogelius pair in the interior of the domain. We prove that the resulting method converges with optimal order, is divergence--free, and is pressure robust. Numerical examples are provided which support the theoretical results.

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Michael Neilan, M. Baris Otus. 2020-08-14. Divergence--free Scott--Vogelius elements on curved domains. https://arxiv.org/abs/2008.06429

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