Convergence Analysis of a Linear, Unconditionally Energy-Stable SAV Finite Element Method for the Cahn-Hilliard Equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908852063043584 |
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| author | Li, Na Zhao, Yongchao |
| author_facet | Li, Na Zhao, Yongchao |
| contents | This paper proposes a finite element scheme, based on the Scalar Auxiliary Variable (SAV) approach, for the Cahn-Hilliard equation--a model that possesses significant physical relevance and a rich mathematical structure. A convergence analysis of the fully discrete scheme is conducted under suitable regularity assumptions, confirming optimal-order convergence in both time and space for the phase variable, chemical potential, and auxiliary variable in the H1-norm. Furthermore, the scheme is proven to be unconditionally energy stable. Finally, a numerical example is presented to demonstrate the effectiveness of the method and to confirm the theoretical convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21574 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of a Linear, Unconditionally Energy-Stable SAV Finite Element Method for the Cahn-Hilliard Equation Li, Na Zhao, Yongchao Numerical Analysis This paper proposes a finite element scheme, based on the Scalar Auxiliary Variable (SAV) approach, for the Cahn-Hilliard equation--a model that possesses significant physical relevance and a rich mathematical structure. A convergence analysis of the fully discrete scheme is conducted under suitable regularity assumptions, confirming optimal-order convergence in both time and space for the phase variable, chemical potential, and auxiliary variable in the H1-norm. Furthermore, the scheme is proven to be unconditionally energy stable. Finally, a numerical example is presented to demonstrate the effectiveness of the method and to confirm the theoretical convergence rates. |
| title | Convergence Analysis of a Linear, Unconditionally Energy-Stable SAV Finite Element Method for the Cahn-Hilliard Equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2602.21574 |