Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential

Abstract

AbstractWe consider numerical approximations for a modified phase field crystal model with a strong nonlinear vacancy potential. Based on the invariant energy quadratization approach and stabilized strategies, we develop linear, unconditionally energy stable numerical schemes using the first‐order Euler method, the second‐order backward differentiation formulas and the second‐order Crank–Nicolson method, respectively. We rigorously prove the unconditional energy stability, the mass conservation of these three numerical schemes and carry out error estimates in time for the first‐order numerical scheme. Various numerical experiments in 2D and 3D are carried out to validate the accuracy, energy stability, mass conservation, and efficiency of the proposed schemes.