A linearly second-order energy stable scheme for the phase field crystal model

Abstract

In this paper, we propose a linear, unconditionally energy stable and second-order (in time) numerical scheme based on a convex splitting scheme and the semi-implicit spectral deferred correction (SISDC) method for the phase field crystal equation. The convex splitting scheme we use is linear, uniquely solvable and unconditionally energy stable but is of first-order, so we take the SISDC method to improve the rate of convergence. The resulted scheme inherits the advantages of the convex splitting scheme and thus leads to linear equations at each time step, which is easy to implement. We also prove that the scheme is unconditionally weak energy stable and of second-order accuracy in time. Numerical experiments are presented to validate the accuracy, efficiency and energy stability of the proposed numerical strategy.