论文期刊

Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation




作者: Qi Li,Liquan Mei,Xiaofeng Yang,Yibao Li
发表/完成日期: 2019-05-30
期刊名称: Advances in Computational Mathematics
期卷: 45
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论文简介
We consider numerical approximations for the modified phase field crystal equation in this paper. The model is a nonlinear damped wave
equation that includes both diffusive dynamics and elastic interactions. To develop easy-to-implement time-stepping schemes with unconditional energy stabilities, we adopt the “Invariant Energy Quadratization”approach. By using the first-order backward Euler, the second-order Crank–Nicolson, and the second-order BDF2 formulas, we obtain three linear and symmetric positive definite schemes. We rigorously prove their unconditional energy stabilities and implement a number of 2D and 3D numerical experiments to demonstrate the accuracy, stability, and efficiency.