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 approximation. 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.

翻译：Scott-Vogelius单元是一种流行的用于离散化Stokes方程且满足inf-sp稳定性并产生无散速度逼近的有限元。然而，众所周知，在区域三角剖分中存在某些临界顶点时，离散压力的收敛速度会恶化。Scott-Vogelius单元的改进形式（如近期提出的压力布线的Stokes单元）同样受此影响。本文针对这些压力空间引入一种简单的修改策略，该策略在保持inf-sup稳定性的同时，使压力以最优速率收敛。