A Decoupled, Linearly Implicit and Unconditionally Energy Stable Scheme for the Coupled Cahn-Hilliard Systems (Journal of Computational Mathematics, 2024)
We present a decoupled, linearly implicit numerical scheme with energy stability andmass conservation for solving the coupled Cahn-Hilliard system. The time-discretization isdone by leap-frog method with the scalar auxiliary variable (SAV) approach. It only needsto solve three linear equations at each time step, where each unknown variable can besolved independently. It is shown that the semi-discrete scheme has second-order accuracyin the temporal direction. Such convergence results are proved by a rigorous analysis ofthe boundedness of the numerical solution and the error estimates at different time-level.Numerical examples are presented to further confirm the validity of the methods.