Mixed hp-finite element approximations on geometric boundary layer meshes in R3

In this paper, we consider the Stokes problem in a three-dimensional polyhedral domain discretized with hp finite elements of type Q(k) for the velocity and Q(k-2) for the pressure, defined on 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 [4,5]. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.