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In this paper, we consider numerical approximations for the anisotropicCahn-Hilliard equation. The main challenge of constructing numerical schemeswith unconditional energy stabilities for this model is how to design propertemporal discretizations for the nonlinear terms with the strong anisotropy. Wepropose two, second order time marching schemes by combining the recentlydeveloped SAV approach with the linear stabilization approach, where threelinear stabilization terms are added. These terms are shown to be crucial toremove the oscillations caused by the anisotropic coefficients, numerically.The novelty of the proposed schemes is that all nonlinear terms can be treatedsemi-explicitly, and one only needs to solve three decoupled linear equationswith constant coefficients at each time step. We further prove theunconditional energy stabilities rigorously, and present various 2D and 3Dnumerical simulations to demonstrate the stability and accuracy.

Efficient schemes with unconditionally energy stability for the  anisotropic Cahn-Hilliard Equation using the stabilized-Scalar Augmented  Variable (S-SAV) approach