Abstract
In this paper, we consider numerical approximations of the Cahn–Hilliard type phase-field crystal model and construct a fully discrete finite element scheme for it. The scheme is the combination of the finite element method for spatial discretization and an invariant energy quadratization method for time marching. It is not only linear and second-order time-accurate, but also unconditionally energy-stable. We prove the unconditional energy stability rigorously and further carry out various numerical examples to demonstrate the stability and the accuracy of the developed scheme numerically.
Highlights
IntroductionCrystallization is a phase change process involving mass transfer from liquid to solid
Numerical Scheme with Second-Crystallization is a phase change process involving mass transfer from liquid to solid.As a powerful modeling tool, the phase-field crystal model (PFC) has been used in this field to simulate the kinetics of atomic crystal growth in the crystallization process for more than two decades; see Elder et al in [1,2]
The total free energy of the PFC model originally comes from the so-called Swift–Hohenberg (SH) model
Summary
Crystallization is a phase change process involving mass transfer from liquid to solid. This paper follows the idea of using the linearized IEQ method for time advancement in [8,9,10,11] and combines it with the spatial finite element method to obtain a fully discrete numerical scheme in time and space. The design purpose of the new variable is to transform the nonlinear part of the energy density function into a quadratic function The advantage of this method is that when the algorithm is designed, all nonlinear terms can be processed in a simple explicit–implicit combination manner. In this way, a linear finite element scheme with second-order accuracy in time can be obtained.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
