A Stabilized Trace FEM for Surface Cahn--Hilliard Equations: Analysis and Simulations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917040685580288 |
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| author | Garg, Deepika Olshanskii, Maxim |
| author_facet | Garg, Deepika Olshanskii, Maxim |
| contents | This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial discretization with an implicit--explicit scheme for temporal discretization. The method belongs to a class of unfitted finite element methods that use a fixed background mesh and a level-set function for implicit surface representation. We establish the numerical stability of the discrete problem by showing a suitable energy dissipation law for it. We further derive optimal-order error estimates assuming simplicial background meshes and finite element spaces of order $m \geq 1$. The effectiveness of the method is demonstrated through numerical experiments on several two-dimensional closed surfaces, confirming the theoretical results and illustrating the robustness and convergence properties of the scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Stabilized Trace FEM for Surface Cahn--Hilliard Equations: Analysis and Simulations Garg, Deepika Olshanskii, Maxim Numerical Analysis 65M60, 65M15, 35K30 This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial discretization with an implicit--explicit scheme for temporal discretization. The method belongs to a class of unfitted finite element methods that use a fixed background mesh and a level-set function for implicit surface representation. We establish the numerical stability of the discrete problem by showing a suitable energy dissipation law for it. We further derive optimal-order error estimates assuming simplicial background meshes and finite element spaces of order $m \geq 1$. The effectiveness of the method is demonstrated through numerical experiments on several two-dimensional closed surfaces, confirming the theoretical results and illustrating the robustness and convergence properties of the scheme. |
| title | A Stabilized Trace FEM for Surface Cahn--Hilliard Equations: Analysis and Simulations |
| topic | Numerical Analysis 65M60, 65M15, 35K30 |
| url | https://arxiv.org/abs/2510.21662 |