  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].
