Here is a follow-up paper on the unconditionally stable time step for diffuse interface methods.

Paper: Maximally fast coarsening algorithms

Authors: Mowei Cheng and Andrew D. Rutenberg

Abstract:

We present maximally fast numerical algorithms for conserved coarsening systems thatare stable and accurate with a growing natural time step \Delta t = A t_{s}^{2/3}. We compare the scaling structure obtained from our maximally fast conserved systems directly against the standard fixed time-step Euler algorithm, and find that the error scales as \sqrt{A}—so arbitrary accuracy can be achieved. For non-conserved systems, only effectively finite time steps are accessible for similar unconditionally stable algorithms.