Preconditioners based on approximation of non-standard norms for phase separation applications

Some of the phase separation processes are typically modeled by well known Cahn-Hilliard equation with obstacle potential. Solving these equations correspond to a nonsmooth and nonlinear optimization problem. Recently a globally convergent Newton Schur method was proposed for the non-linear Schur complement corresponding to this 2 × 2 non-linear system. The discrete linear problem has essentially three parameters: the mesh size, time step, and a parameter related to interface width. The preconditioners considered so far has not been robust to one of these parameters. We propose preconditioners that seem to be robust provided the mesh is sufficiently refined.