Structure-preserving weighted BDF2 methods for Anisotropic Cahn-Hilliard model: uniform/variable-time-steps
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| Format: | Preprint |
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2024
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| _version_ | 1866911918958051328 |
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| author | Li, Meng Bi, Jingjiang Wang, Nan |
| author_facet | Li, Meng Bi, Jingjiang Wang, Nan |
| contents | In this paper, we innovatively develop uniform/variable-time-step weighted and shifted BDF2 (WSBDF2) methods for the anisotropic Cahn-Hilliard (CH) model, combining the scalar auxiliary variable (SAV) approach with two types of stabilized techniques. Using the concept of $G$-stability, the uniform-time-step WSBDF2 method is theoretically proved to be energy-stable. Due to the inapplicability of the relevant G-stability properties, another technique is adopted in this work to demonstrate the energy stability of the variable-time-step WSBDF2 method. In addition, the two numerical schemes are all mass-conservative.Finally, numerous numerical simulations are presented to demonstrate the stability and accuracy of these schemes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_13259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structure-preserving weighted BDF2 methods for Anisotropic Cahn-Hilliard model: uniform/variable-time-steps Li, Meng Bi, Jingjiang Wang, Nan Numerical Analysis In this paper, we innovatively develop uniform/variable-time-step weighted and shifted BDF2 (WSBDF2) methods for the anisotropic Cahn-Hilliard (CH) model, combining the scalar auxiliary variable (SAV) approach with two types of stabilized techniques. Using the concept of $G$-stability, the uniform-time-step WSBDF2 method is theoretically proved to be energy-stable. Due to the inapplicability of the relevant G-stability properties, another technique is adopted in this work to demonstrate the energy stability of the variable-time-step WSBDF2 method. In addition, the two numerical schemes are all mass-conservative.Finally, numerous numerical simulations are presented to demonstrate the stability and accuracy of these schemes. |
| title | Structure-preserving weighted BDF2 methods for Anisotropic Cahn-Hilliard model: uniform/variable-time-steps |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.13259 |