Robust Multigrid Preconditioning for Parameter-Dependent Problems I: The Stokes-Type Case

Parameter dependent problems can be discretiaed by selective reduced integration methods tn achieve parameter independent discretisation errors. The convergence rate of standard multigrid solvers applied to the primal linear system deteriorates, if the parameter becomes small. In this paper, we construct multigrid components leading to parameter independent rates. We need a robust base iteration as smoother and uniformly continuous grid transfer operations. The suggested multigrid preconditioner is applied to problems from linear elasticity.