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

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.