In this note we propose a discretization of the Stokes equations which is inf-sup stable on general polygonal or polyhedral meshes and robust with respect to the presence of large irrotational source terms. The key idea is to construct a discrete space for the velocity which extends two important properties of the Crouzeix-Raviart element to general meshes, namely the continuity of mean values at interfaces and the approximation of nontrivial solenoidal fields. As a result, it is proved that the approximation of the velocity is not affected by the presence of the irrotational part of the source term. A numerical validation of the theoretical results is provided.
