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Divergence--free Scott--Vogelius elements on curved domains (2008.06429v1)
Published 14 Aug 2020 in math.NA and cs.NA
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.