  We construct several stable finite element pairs for the Stokes problem on
barycentric refinements in arbitrary dimensions. A key feature of the spaces is
that the divergence maps the discrete velocity space onto the the discrete
pressure space; thus, when applied to models of incompressible flows, the pairs
yield divergence-free velocity approximations. The key result is a local
inf-sup stability that holds for any dimension and for any polynomial degree.
With this result, we construct global divergence-free and stable pairs in
arbitrary dimension and for any polynomial degree.
