Unconditional energy stability and temporal convergence of first-order numerical scheme for the square phase-field crystal model

Abstract

This paper presents a sixth-order nonlinear parabolic problem of the square phase-field crystal model. We first demonstrate the time-discrete backward Euler scheme with mass conservation and energy stability. Then, we prove the unconditionally optimal error estimates for the time-discrete backward Euler scheme. In the end, we present 2D and 3D numerical simulations to confirm the theoretical results.