INF-SUP STABLE FINITE ELEMENTS ON BARYCENTRIC REFINEMENTS PRODUCING DIVERGENCE-FREE APPROXIMATIONS IN ARBITRARY DIMENSIONS

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 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.