| Error Estimate of Full-Discrete Numerical Scheme for the Nonlocal Allen-Cahn Model |
| Received:May 11, 2023 Revised:September 23, 2023 |
| Key Words:
nonlocal Allen-Cahn model uniquely solvable unconditionally energy stable error estimate numerical tests
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.12261017; 62062018), the Foundation of Science and Technology of Guizhou Province (Grant No.ZK[2022]031) and the Scientific Research Foundation of Guizhou University of Finance and Economics (Grant Nos.2022KYYB08; 2022ZCZX077). |
| Author Name | Affiliation | | Jun ZHANG | School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China | | Xiaohu YANG | The Meteorological Disaster Prevention Center of Guizhou Province, Guizhou 558399, P. R. China | | Fulin MEI | Xi'an Institute of Applied Optics, Shaanxi 710000, P. R. China | | Zhimei JI | Financial Department, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China | | Yu ZHANG | School of Mathematics and Statistics, 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 Energy Quadratization (IEQ) method. We demonstrate that the proposed fully discrete numerical method is uniquely solvable, unconditionally energy stable, and obtain the optimal error estimate of the scheme for both space and time. Additionally, we conduct several numerical tests to verify the theoretical results. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.03.007 |
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