P. Letallec et A. Patra, NONOVERLAPPING DOMAIN DECOMPOSITION METHODS FOR ADAPTIVE HP APPROXIMATIONS OF THE STOKES PROBLEM WITH DISCONTINUOUS PRESSURE FIELDS, Computer methods in applied mechanics and engineering, 145(3-4), 1997, pp. 361-379
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.