  Recently, Garcke et al.[Garcke, Hinze, Kahle, A stable and linear time
discretization for a thermodynamically consistent model for two-phase
incompressible flow, Applied Numerical Mathematics 99, pp. 151-171, 2016]
developed a consistent discretization scheme for a thermodynamically consistent
diffuse interface model for incompressible two-phase flows with different
densities. At the heart of this method lies the solution of large and sparse
linear systems that arise in a semismooth Newton method.
  We propose the use of preconditioned Krylov subspace solvers using effective
Schur complement approximations. Numerical results illustrate the efficiency of
our approach. In particular, our preconditioner is shown to be robust with
respect to parameter changes.
