The resolution of the incompressible Navier-Stokes equations is tricky, and it is well known that one of the major issue is to compute a divergence free velocity. The non-conforming Crouzeix-Raviart finite element are convenient since they induce local mass conservation. Moreover they are such that the stability constant of the Fortin operator is equal to 1. This implies that they can easily handle anisotropic mesh [1, 2]. However spurious velocities may appear and damage the approximation. We propose a scheme here that allows to reduce the spurious velocities. It is based on a new discretisation for the gradient of pressure based on the symmetric MPFA scheme (finite volume MultiPoint Flux Approximation) [3, 4, 5].

翻译：不可压缩Navier-Stokes方程的求解具有挑战性，其中一个主要难点在于计算无散度速度场。非协调Crouzeix-Raviart有限元由于具有局部质量守恒性而十分便利。此外，其Fortin算子的稳定性常数等于1，因此能够轻松处理各向异性网格[1,2]。然而，该格式可能出现伪速度并影响近似精度。本文提出了一种可减少伪速度的新格式，该格式基于对称MPFA格式（多点多通量近似有限体积法）[3,4,5]实现了新的压力梯度离散化方案。