Efficient and linear schemes for anisotropic Cahn-Hilliard model using the Stabilized-Invariant Energy Quadratization (S-IEQ) approach

In this paper, we consider numerical approximations for the anisotropic Cahn-Hilliard equation. We develop two linear and second-order schemes that combine the IEQ approach with the stabilization technique, where several extra linear stabilization terms are added in and they can be shown to be crucial to suppress the non-physical spatial oscillations caused by the strong anisotropy. We show the well-posedness of the resulting linear systems and further prove their corresponding unconditional energy stabilities rigorously. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy, and efficiency of the proposed schemes. (C) 2018 Elsevier B.V. All rights reserved.