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2007-02

Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes

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