On the stability and accuracy of partially and fully implicit schemes for phase field modeling

We study in this paper the accuracy and stability of partially and fully implicit schemes for phase field modeling. Through theoretical and numerical analysis of Allen–Cahn and Cahn–Hilliard models, we investigate the potential problems of using partially implicit schemes, demonstrate the importance of using fully implicit schemes and discuss the limitation of energy stability that are often used to evaluate the quality of a numerical scheme for phase-field modeling. In particular, we make the following observations: