An unconditionally energy stable second order finite element method for solving the Allen-Cahn equation

In this paper, we design, analyze and numerically validate an unconditionally energy stable second order numerical method for solving the Allen-Cahn equation which represents a model for anti-phase domain coarsening in a binary alloy. The proposed scheme inherits the property of the decrease of the total energy from the Allen-Cahn equation. An error estimate for the fully discretized scheme is also established. Numerical examples are presented to confirm the accuracy, efficiency, and stability of the proposed method. In particular, the method is shown to be unconditionally energy stable and second order accurate in both time and space discretizations. (C) 2018 Elsevier B.V. All rights reserved.