Two finite difference schemes for the phase field crystal equation
Two finite difference schemes for the phase field crystal equation
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DOI：
10.1007/s11425-015-5025-1
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发表时间：
2015-05
期刊：
影响因子：
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通讯作者：
Hai-Yan Cao;Zhi‐zhong Sun
中科院分区：
文献类型：
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作者：
Hai-Yan Cao;Zhi‐zhong Sun
相场晶体（PFC）模型是一个空间上的六阶非线性演化方程。在第一部分中，我们导出了一个三层线性化差分格式，然后利用能量方法结合归纳法证明了该格式是能量稳定的，唯一可解的，并且在L2范数下是二阶收敛的。在第二部分中，我们分析了Zhang等人在2013年提出的一个两层非线性差分格式的唯一可解性和收敛性。给出了一些数值结果并进行了比较。
The phase field crystal (PFC) model is a nonlinear evolutionary equation that is of sixth order in space. In the first part of this work, we derive a three level linearized difference scheme, which is then proved to be energy stable, unique solvable and second order convergent inL2norm by the energy method combining with the inductive method. In the second part of the work, we analyze the unique solvability and convergence of a two level nonlinear difference scheme, which was developed by Zhang et al. in 2013. Some numerical results with comparisons are provided.