Stability and error estimates of GPAV-based unconditionally energy-stable scheme for phase field crystal equation

Abstract

In this article, we propose a linear, second-order, semi-discrete time stepping scheme for the phase field crystal equation based on generalized positive auxiliary variable (GPAV) approach. This scheme reduces the operation counts by half compared to the GPAV and the scalar auxiliary variable methods in previous works. We prove the unconditionally energy stability and provide bounds and error estimates for the field function. Numerical experiments are carried out to verify our theoretical results and demonstrate the robustness and accuracy of the proposed scheme.