Mixed hp-DGFEM for incompressible flows II: Geometric edge meshes

Abstract

We consider the Stokes problem in three-dimensional polyhedral domains discretized on hexahedral meshes with hp-discontinuous Galerkin finite elements of type IQk for the velocity and IQk-1 for the pressure. We prove that these elements are inf-sup stable on geometric edge meshes that are refined anisotropically and non quasi-uniformly towards edges and corners. The discrete inf-sup constant is shown to be independent of the aspect ratio of the anisotropic elements and is of order {\mathcal O}(k-3/2) in the polynomial degree k, as in the case of IQk-IQk-2 conforming approximations on the same meshes.