Uniform preconditioners for a parameter dependent saddle point problem with application to generalized Stokes interface equations

We consider an abstract parameter dependent saddle-point problem and present a general framework for analyzing robust Schur complement preconditioners. The abstract analysis is applied to a generalized Stokes problem, which yields robustness of the Cahouet-Chabard preconditioner. Motivated by models for two-phase incompressible flows we consider a generalized Stokes interface problem. Application of the general theory results in a new Schur complement preconditioner for this class of problems. The robustness of this preconditioner with respect to several parameters is treated. Results of numerical experiments are given that illustrate robustness properties of the preconditioner.