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

作     者：Xiaowei Chen Xu Qian Songhe Song 

作者机构：Department of MathematicsNational University of Defense TechnologyChangshaHunan 410073China 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2023年第15卷第1期

页      面：159-181页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：the National Key R&D Program of China(No.2020YFA0709800) the National Key Project(No.GJXM92579) the National Natural Science Foundation of China(No.12071481)。 

主　　题：Maximum-principle-preserving mass-conserving scheme the conservative AllenCahn equation 

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.