一维Allen-Cahn方程Du Fort-Frankel格式的离散最大化原则和能量稳定性研究
Discrete Maximum Principle and Energy Stability Analysis of Du Fort-Frankel Scheme for 1D Allen-Cahn Equation
DOI: 10.12677/PM.2022.129164, PDF,    国家自然科学基金支持
作者: 林树华：南昌航空大学，数学与信息科学学院，江西 南昌
关键词: Allen-Cahn方程；Du Fort-Frankel格式；离散最大化原则；离散能量稳定性；Allen-Cahn Equation； Du Fort-Frankel Difference Schemes； Maximum Principle； Energy Stability
摘要: 本文研究一维非线性Allen-Cahn方程的保结构Du Fort-Frankel差分法。该格式是显式的且无条件能量稳定。所得的数值解满足离散最大化原则。运用离散最大化原则得到该格式在L2范数下有O(τ2+h2+τ2/h2)的收敛阶。最后，数值算例验证了理论结果。
Abstract: In this paper, we consider the structure preserving Du Fort-Frankel difference schemes for one dimensional nonlinear Allen-Cahn equation. The scheme is explicit and unconditionally energy stable. The numerical solution satisfies the principle of discrete maximum. The convergence order of the scheme is O(τ2+h2+τ2/h2) under L2 norm. Finally, numerical examples verify the theoretical results.
文章引用：林树华. 一维Allen-Cahn方程Du Fort-Frankel格式的离散最大化原则和能量稳定性研究[J]. 理论数学, 2022, 12(9): 1501-1511. https://doi.org/10.12677/PM.2022.129164

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