Numerical approximation of SAV finite difference method for the Allen–Cahn equation

In this paper, the second-order scalar auxiliary variable approach combined with finite difference method is employed for the Allen–Cahn equation that represents a phenomenological model for antiphase domain coarsening in a binary mixture. The second-order backward differentiation formula is used in time. The error estimation of the semi-discrete scheme is derived in the sense of [Formula: see text]-norm. Several numerical simulations in 2D and 3D are demonstrated to verify the accuracy and efficiency of the proposed scheme.