Fully discrete spectral-Galerkin linear and unconditionally energy stable algorithm for the square phase-field crystal system

Abstract

We consider developing a fully discrete type numerical algorithm for the square phase-field crystal system in this article. The scheme is based on the combination of the spectral-Galerkin method for spatial discretization and an invariant energy quadratization (IEQ) method for time marching. The obtained scheme consists of several decoupled, constant-coefficient linear equations with second-order temporal convergence rate and unconditional energy stability. We prove the unconditional energy stability rigorously and further carry out various numerical examples to demonstrate the effectiveness of the developed scheme, numerically.