A uniformly stable Fortin operator for the Taylor-Hood element

We construct a new Fortin operator for the lowest order Taylor–Hood element, which is uniformly stable both in L and H. The construction, which is restricted to two space dimensions, is based on a tight connection between a subspace of the Taylor– Hood velocity space and the lowest order Nedelec edge element. General shape regular triangulations are allowed for the H–stability, while some mesh restrictions are imposed to obtain the L–stability. As a consequence of this construction, a uniform inf–sup condition associated the corresponding discretizations of a parameter dependent Stokes problem is obtained, and we are able to verify uniform bounds for a family of preconditioners for such problems, without relying on any extra regularity ensured by convexity of the domain.