The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element

The Scott-Vogelius finite element pair for the numerical discretization of the stationary Stokes equation in 2D is a popular element which is based on a continuous velocity approximation of polynomial order \(k\) and a discontinuous pressure approximation of order \(k-1\). It employs a "singular distance" (measured by some geometric mesh quantity \( \Theta \left( \mathbf{z}\right) \geq 0\) for triangle vertices \(\mathbf{z}\)) and imposes a local side condition on the pressure space associated to vertices \(\mathbf{z}\) with \(\Theta \left( \mathbf{z}\right) =0\). The method is inf-sup stable for any fixed regular triangulation and \(k\geq 4\). However, the inf-sup constant deteriorates if the triangulation contains nearly singular vertices \(0