A second-order linear unconditionally energy-stable scheme for the phase field crystal equation

This paper presents a linear implicit scheme for numerically solving the phase field crystal (PFC) equation. The scheme is constructed by the scalar auxiliary variable (SAV) approach and the leapfrog scheme in temporal direction. The proposed scheme is decoupled, and it is easy to be implemented. In contrast, the previous SAV-type schemes for the PFC equation are usually coupled. The scheme satisfies the energy stability at the discrete level. Moreover, it is proved that the scheme is convergent with second-order accuracy in the temporal direction. Several numerical examples are carried out to confirm the theoretical results.