Pressure-improved Scott–Vogelius type elements

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.