Mixed hp-finite element approximations on geometric boundary layer meshes in R-3

In this paper, we consider the Stokes problem in a three-dimensional polyhe dral domain discretized with hp finite elements of type Q(k) for the veloci ty and Q(k-2) for the pressure, defined on meshes anisotropically and non-q uasi-uniformly refined towards faces, edges, and corners. The inf-sup const ant of the discretized problem is independent of arbitrarily large aspect r atios and exhibits the same dependence on k as in in the case of isotropica lly refined meshes. Our work generalizes a recent result for two-dimensiona l problems in [4,5]. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.