修正的晶体相场方程的无条件能量稳定数值格式  

An Unconditionally Energy Stable Numerical Scheme for the Modified Phase Field Crystal Equation

作　　者：梁译泓 贾宏恩 Liang Yihong;Jia Hongen(School of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China;Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology,Jinzhong 030619,China)

机构地区：[1]太原理工大学数学学院,晋中030600 [2]智能优化计算与区块链技术山西省重点实验室,晋中030619

出　　处：《数学理论与应用》2023年第4期59-75,共17页Mathematical Theory and Applications

基　　金：山西省归国留学基金项目(No.2021-029);山西省科技合作交流专项项目(No.202104041101019)资助。

摘　　要：针对具有周期边界条件的修正的晶体相场方程,本文构建一个线性、二阶、无条件能量稳定的时间半离散数值格式,通过引入拉格朗日乘子处理非线性项,使用Crank-Nicolson方法进行时间离散,依次证明该数值格式的唯一可解性、无条件能量稳定性及在时间上的二阶无条件收敛性,最后通过数值算例对该格式的有效性进行验证.This paper constructs a linear,second-order,unconditionally energy stable,semi-discrete time stepping scheme for the modified phase field crystal equation with periodic boundary conditions.The unique solvability,unconditionally energy stability and unconditionally temporal convergence of order 2 of the numerical scheme are showed by introducing a Lagrange multiplier to deal with the nonlinear terms and adopting the second-order Crank-Nicolson method to discrete time.Numerical experiments are given in the last section to validate the efficiency of the proposed scheme.

关 键 词：修正的晶体相场方程 线性格式 无条件能量稳定 误差估计 

分 类 号：O241.82[理学—计算数学]