scholarly journals Error estimates for second-order SAV finite element method to phase field crystal model

2021 ◽  
Vol 29 (1) ◽  
pp. 1735-1752
Author(s):  
Liupeng Wang ◽  
◽  
Yunqing Huang ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Phase Field ◽  
Second Order ◽  
Crystal Model ◽  
Element Method ◽  
Phase Field Crystal

scholarly journals Efficient Fully Discrete Finite-Element Numerical Scheme with Second-Order Temporal Accuracy for the Phase-Field Crystal Model

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 155
Author(s):  
Jun Zhang ◽  
Xiaofeng Yang
Keyword(s):  
Finite Element ◽  
Phase Field ◽  
Second Order ◽  
The Finite Element Method ◽  
Fully Discrete ◽  
Crystal Model ◽  
Time Marching ◽  
The Stability ◽  
Discrete Finite Element ◽  
Phase Field Crystal

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.

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