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

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

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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.

nonlocal Allen-Cahn modeluniquely solvableunconditionally energy stableerror estimatenumerical tests

Jun ZHANG、Xiaohu YANG、Fulin MEI、Zhimei JI、Yu ZHANG

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School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guizhou 550025,P.R.China

The Meteorological Disaster Prevention Center of Guizhou Province,Guizhou 558399,P.R.China

Xi'an Institute of Applied Optics,Shaanxi 710000,P.R.China

Financial Department,Guizhou University of Finance and Economics,Guizhou 550025,P.R.China

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National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaFoundation of Science and Technology of Guizhou ProvinceScientific Research Foundation of Guizhou University of Finance and EconomicsScientific Research Foundation of Guizhou University of Finance and Economics

1226101762062018ZK[2022]0312022KYYB082022ZCZX077

2024

10.3770/j.issn:2095-2651.2024.03.007

数学研究及应用
大连理工大学

数学研究及应用

影响因子：0.094
ISSN：2095-2651
年,卷(期)：2024.44(3)
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