Non-overlapping domain decomposition methods for adaptive hp approximations of the Stokes problem with discontinuous pressure fields

This paper proposes a framework for non-overlapping domain decomposition methods applied to viscous incompressible flows governed by Stokes equations modelled by the hp version of the finite element method. Preconditioning methods developed earlier for elliptic problems are extended to this case. Suitable condition number bounds are obtained for both the hierarchical hp preconditioners of the type proposed in [9] and Neumann-Neumann preconditioners proposed in [10]. Systematic procedures for constructing compatible hp approximations for incompressible flow are also described.