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