Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation
The Allen-Cahn model is discussed mainly in the phase field simulation. The compact difference method will be used to numerically approximate the two-dimensional nonlinear Allen-Cahn equation with initial and boundary value conditions, and then, a fully discrete compact difference scheme with second...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/8522231 |
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| _version_ | 1832567183679422464 |
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| author | Yu Bo Dan Tian Xiao Liu Yuanfeng Jin |
| author_facet | Yu Bo Dan Tian Xiao Liu Yuanfeng Jin |
| author_sort | Yu Bo |
| collection | DOAJ |
| description | The Allen-Cahn model is discussed mainly in the phase field simulation. The compact difference method will be used to numerically approximate the two-dimensional nonlinear Allen-Cahn equation with initial and boundary value conditions, and then, a fully discrete compact difference scheme with second-order accuracy in time and fourth-order in space is established. And its numerical solution satisfies the discrete maximum principle under the constraints of reasonable space and time steps. On this basis, the energy stability of the scheme is investigated. Finally, numerical examples are given to illustrate the theoretical results. |
| format | Article |
| id | doaj-art-9a3a8d12778e45f8a3cde2984dd929a7 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9a3a8d12778e45f8a3cde2984dd929a72025-02-03T01:02:14ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/8522231Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn EquationYu Bo0Dan Tian1Xiao Liu2Yuanfeng Jin3College of SciencePublic Course DepartmentCollege of ScienceCollege of ScienceThe Allen-Cahn model is discussed mainly in the phase field simulation. The compact difference method will be used to numerically approximate the two-dimensional nonlinear Allen-Cahn equation with initial and boundary value conditions, and then, a fully discrete compact difference scheme with second-order accuracy in time and fourth-order in space is established. And its numerical solution satisfies the discrete maximum principle under the constraints of reasonable space and time steps. On this basis, the energy stability of the scheme is investigated. Finally, numerical examples are given to illustrate the theoretical results.http://dx.doi.org/10.1155/2022/8522231 |
| spellingShingle | Yu Bo Dan Tian Xiao Liu Yuanfeng Jin Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation Journal of Function Spaces |
| title | Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation |
| title_full | Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation |
| title_fullStr | Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation |
| title_full_unstemmed | Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation |
| title_short | Discrete Maximum Principle and Energy Stability of the Compact Difference Scheme for Two-Dimensional Allen-Cahn Equation |
| title_sort | discrete maximum principle and energy stability of the compact difference scheme for two dimensional allen cahn equation |
| url | http://dx.doi.org/10.1155/2022/8522231 |
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