Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation

被引：0
|
作者：
Chen, Xiaowei [1 ]
Qian, Xu [1 ]
Song, Songhe [1 ]
机构：
[1] Natl Univ Def Technol, Dept Math, Changsha 410073, Hunan, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2022年
基金：
国家重点研发计划; 中国国家自然科学基金;
关键词：
Maximum-principle-preserving; mass-conserving scheme; the conservative Allen-Cahn equation; TIME DIFFERENCING SCHEMES; PHASE-TRANSITIONS; MOTION; MODEL;
D O I：
10.4208/aamm.OA-2021-0325xxx202x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order finite-difference semidiscretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is verified by several numerical examples.
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页数：23
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