具有一般流动性的艾伦-卡恩方程的线性二阶无条件最大约束原则保留方案

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Dianming Hou , Tianxiang Zhang , Hongyi Zhu
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引用次数: 0

摘要

在这项工作中,我们研究了具有一般流动性的 Allen-Cahn 方程的线性二阶数值方法。所提出的方案结合了用于时间逼近的两步式一阶和二阶后向微分公式以及用于空间离散化的中心有限差分法,还包括两个额外的稳定项。在相邻时间步长比和两个稳定参数的温和约束下,数值方案的离散最大约束原理得到了严格证明。此外,我们还得到了恒定流动性情况下的 H1 规范误差估计和一般流动性情况下的 L∞ 规范误差估计,以及这两种情况下的能量稳定性。最后,我们进行了大量的数值实验来验证理论结果,并开发了一种自适应时间步进策略来证明所提方法的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A linear second order unconditionally maximum bound principle-preserving scheme for the Allen-Cahn equation with general mobility

In this work, we investigate a linear second-order numerical method for the Allen-Cahn equation with general mobility. The proposed scheme is a combination of the two-step first- and second-order backward differentiation formulas for time approximation and the central finite difference for spatial discretization, two additional stabilizing terms are also included. The discrete maximum bound principle of the numerical scheme is rigorously proved under mild constraints on the adjacent time-step ratio and the two stabilization parameters. Furthermore, the error estimates in H1-norm for the case of constant mobility and L-norm for the general mobility case, as well as the energy stability for both cases are obtained. Finally, we present extensive numerical experiments to validate the theoretical results, and develop an adaptive time-stepping strategy to demonstrate the performance of the proposed method.

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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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