Pressure-improved Scott-Vogelius type elements
Nis-Erik Bohne1, Benedikt Gräßle1, Stefan A Sauter1
1Institut für Mathematik, Universität Zürich, Winterthurerstr 190, 8057 Zürich, Switzerland.
Abstract:
The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximations. However, it is well known that the convergence rates for the discrete pressure deteriorate in the presence of certain critical vertices in a triangulation of the domain. Modifications of the Scott-Vogelius element such as the recently introduced pressure-wired Stokes element also suffer from this effect. In this paper we introduce a simple modification strategy for these pressure spaces that preserves the inf-sup stability while the pressure converges at an optimal rate.
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