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

2020/08/14 by Michael Neilan, Neilan, Michael, M. Baris Otus +1 · 3 citations
Computer Science · Mathematics · #65N30 #76M10 #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA #msc:65N30 #msc:76M10

paper · pdf · doi:10.48550/arxiv.2008.06429

arxiv created 2020/08/14 · arxiv updated 2020/08/17

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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