Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916115166265344 |
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| author | Chen, Yaoyao Liu, Hailiang Yi, Nianyu Yin, Peimeng |
| author_facet | Chen, Yaoyao Liu, Hailiang Yi, Nianyu Yin, Peimeng |
| contents | In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy for solving both the Cahn-Hilliard equation and the Allen-Cahn equation. For time discretization, we compare three distinct IEQ-FEM schemes that position the intermediate function introduced by the IEQ approach in different function spaces: finite element space, continuous function space, or a combination of these spaces. Rigorous proofs establishing the existence and uniqueness of the numerical solution, along with analyses of energy dissipation for both equations and mass conservation for the Cahn-Hilliard equation, are provided. The proposed schemes' accuracy, efficiency, and solution properties are demonstrated through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation Chen, Yaoyao Liu, Hailiang Yi, Nianyu Yin, Peimeng Numerical Analysis In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy for solving both the Cahn-Hilliard equation and the Allen-Cahn equation. For time discretization, we compare three distinct IEQ-FEM schemes that position the intermediate function introduced by the IEQ approach in different function spaces: finite element space, continuous function space, or a combination of these spaces. Rigorous proofs establishing the existence and uniqueness of the numerical solution, along with analyses of energy dissipation for both equations and mass conservation for the Cahn-Hilliard equation, are provided. The proposed schemes' accuracy, efficiency, and solution properties are demonstrated through numerical experiments. |
| title | Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.02712 |