Unconditionally energy stable invariant energy quadratization finite element methods for Phase-Field Crystal equation and Swift–Hohenberg equation

Abstract

In this paper, we design, analyze and numerically validate linearly first- and second-order unconditionally energy stable numerical methods for solving the Phase-Field Crystal equation and Swift–Hohenberg equation which describe a multitude of processes involving spatiotemporal pattern formation. The properties of well-posedness of solution and the decrease of the total energy for the fully discretized schemes are established. Numerical examples are presented to confirm the accuracy, efficiency, and stability of the proposed method.