Mixed hp-finite element approximations on geometric edge and boundary layer meshes in three dimensions

In this paper, we consider the Stokes problem in a three-dimensional polyhedral domain discretized with hp finite elements of type Qk for the velocity and Qk-2 for the pressure, defined on hexahedral meshes anisotropically and non quasi-uniformly refined towards faces, edges, and corners. The inf-sup constant of the discretized problem is independent of arbitrarily large aspect ratios and exhibits the same dependence on k as in in the case of isotropically refined meshes. Our work generalizes a recent result for two-dimensional problems in [8,9]