数学研究及应用2024，Vol.44Issue(3) ：344-358.DOI:10.3770/j.issn:2095-2651.2024.03.007

Error Estimate of Full-Discrete Numerical Scheme for the Nonlocal Allen-Cahn Model

Jun ZHANG Xiaohu YANG Fulin MEI Zhimei JI Yu ZHANG
数学研究及应用2024，Vol.44Issue(3) ：344-358.DOI:10.3770/j.issn:2095-2651.2024.03.007
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Error Estimate of Full-Discrete Numerical Scheme for the Nonlocal Allen-Cahn Model

Jun ZHANG 1Xiaohu YANG 2Fulin MEI 3Zhimei JI 4Yu ZHANG1
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作者信息

  • 1. School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guizhou 550025,P.R.China
  • 2. The Meteorological Disaster Prevention Center of Guizhou Province,Guizhou 558399,P.R.China
  • 3. Xi'an Institute of Applied Optics,Shaanxi 710000,P.R.China
  • 4. Financial Department,Guizhou University of Finance and Economics,Guizhou 550025,P.R.China
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Abstract

In this work,we study the error estimates of the fully discrete Fourier pseudo-spectral numerical scheme for solving the nonlocal volume-conserved Allen-Cahn(AC)equation.The time marching method of the numerical scheme is based on the well-known Invariant En-ergy Quadratization(IEQ)method.We demonstrate that the proposed fully discrete numerical method is uniquely solvable,unconditionally energy stable,and obtain the optimal error esti-mate of the scheme for both space and time.Additionally,we conduct several numerical tests to verify the theoretical results.

Key words

nonlocal Allen-Cahn model/uniquely solvable/unconditionally energy stable/error estimate/numerical tests

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基金项目

National Natural Science Foundation of China(12261017)

National Natural Science Foundation of China(62062018)

Foundation of Science and Technology of Guizhou Province(ZK[2022]031)

Scientific Research Foundation of Guizhou University of Finance and Economics(2022KYYB08)

Scientific Research Foundation of Guizhou University of Finance and Economics(2022ZCZX077)

出版年

2024
数学研究及应用
大连理工大学

数学研究及应用

CSCD
影响因子：0.094
ISSN：2095-2651
参考文献量32
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