Multiple discretisation multilevel methods applied to the Stokes problem

We consider a general framework for analysing the convergence of multilevel solvers applied to finite element discretisations of the Stokes problem, both of conforming and nonconforming type. As a basic new feature, our approach allows to use different finite element discretisations on each level of the multigrid hierarchy. Thus, in our multiple discretisation multilevel approach, higher order finite element discretisations can be combined with fast multi-level solvers based on lower order (nonconforming) finite elements. This leads to the design of efficient multi-level solvers for higher order finite element discretisations.