数学
离散化
有限元法
守恒定律
质量守恒
应用数学
最大值原理
能量守恒
龙格-库塔方法
数值分析
空格(标点符号)
限制器
理论(学习稳定性)
磁通限制器
数学分析
数学优化
计算机科学
物理
最优控制
热力学
电信
量子力学
机器学习
操作系统
作者
Jing Yang,Nianyu Yi,Hong Zhang
标识
DOI:10.1016/j.apnum.2023.03.002
摘要
In this paper, based on the mass-lumping finite element space discretization, we incorporate the integrating factor Runge–Kutta method and stabilization technique to develop a class of temporal up to the fourth-order unconditionally structure-preserving schemes for the Allen–Cahn equation and its conservative forms. The proposed methods are linear, without requiring any post-processing or limiters, and unconditionally preserve the maximum principle and mass conservation law. Several numerical experiments verify the high-order temporal accuracy of the proposed schemes, as well demonstrate the ability to preserve the maximum principle, mass conservation, and energy stability over long periods. Moreover, by the aid of numerical simulation, we show that the proposed schemes also have good performances in terms of structure-preserving with high order finite element method.
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