On preconditioned Uzawa-type iterations for a saddle point problem with inequality constraints

Abstract

We consider preconditioned Uzawa iterations for a saddle point Problem with inequality constraints as arising from an implicit time discretization of the Cahn-Hilliard equation with obstacle potential. We present a new class of preconditioners based on linear Schur complements associated with successive approximations of the coincidence set. In numerical experiments, we found superlinear convergence and finite termination.