NONOVERLAPPING DOMAIN DECOMPOSITION METHODS FOR ADAPTIVE HP APPROXIMATIONS OF THE STOKES PROBLEM WITH DISCONTINUOUS PRESSURE FIELDS

This paper proposes a framework for non-overlapping domain decompositi on methods applied to viscous incompressible flows governed by Stokes equations modelled by the hp version of the finite element method. Pre conditioning methods developed earlier for elliptic problems are exten ded to this case. Suitable condition number bounds are obtained for bo th the hierarchical hp preconditioners of the type proposed in [9] and Neumann-Neumann preconditioners proposed in [10]. Systematic procedur es for constructing compatible hp approximations for incompressible fl ow are also described.