Mixed hp-FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes

The divergence stability of mixed hp Finite Element Methods for incompressi ble fluid flow is analyzed. A discrete inf-sup condition is proved for a ge neral class of meshes. The meshes may be refined anisotropically, geometric ally and may contain hanging nodes on geometric patches. The inf-sup consta nt is shown to be independent of the aspect ratio of the anisotropic elemen ts and the dependence on the polynomial degree is analyzed. Numerical estim ates of inf-sup constants confirm the theoretical results.