by Schieweck, F..

**Series:** 2007-02, Preprints

- MSC:
- 65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
- 65N35 Spectral, collocation and related methods
- 76D07 Stokes and related (Oseen, etc.) flows

**Abstract:**

We consider a family of quadrilateral or hexahedral

mixed hp-finite elements for an incompressible

flow problem with $Q_r$-elements for the velocity and

discontinuous $P_{r-1}$-elements for the pressure where the order

$r$ can vary from element to element

between $2$ and an arbitrary bound.

For multilevel adaptive grids

with hanging nodes and a sufficiently small mesh size,

we prove the inf-sup condition uniformly with respect to the mesh

size and the polynomial degree.

**Keywords:**

Stokes problem, inf-sup condition, mixed hp-FEM, quadrilateral and hexahedral finite elements, multilevel adaptive grids, hanging nodes