High-order temporal parametric finite element methods for simulating solid-state dewetting
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| Format: | Preprint |
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2025
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| _version_ | 1866917026475278336 |
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| author | Gan, Xiaowen Teng, Yuqian Wang, Sisheng |
| author_facet | Gan, Xiaowen Teng, Yuqian Wang, Sisheng |
| contents | We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point migration, along with appropriate boundary conditions. By incorporating the predictor-corrector strategy and the backward differentiation formula for time discretization into the energy-stable parametric finite element method developed by Zhao et al. (2021), we successfully construct temporally high-order schemes. The resulting numerical scheme is semi-implicit, requiring the solution of a linear system at each time step. The well-posedness of the fully discretized system is established. Moreover, the method maintains the long-term mesh equidistribution property. Extensive numerical experiments demonstrate that our methods achieve the desired temporal accuracy, measured by the manifold distance, while maintaining good mesh quality throughout the evolution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_16493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-order temporal parametric finite element methods for simulating solid-state dewetting Gan, Xiaowen Teng, Yuqian Wang, Sisheng Numerical Analysis Mathematical Physics 65M60, 65M12, 35K25 G.1.8; G.1.10 We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point migration, along with appropriate boundary conditions. By incorporating the predictor-corrector strategy and the backward differentiation formula for time discretization into the energy-stable parametric finite element method developed by Zhao et al. (2021), we successfully construct temporally high-order schemes. The resulting numerical scheme is semi-implicit, requiring the solution of a linear system at each time step. The well-posedness of the fully discretized system is established. Moreover, the method maintains the long-term mesh equidistribution property. Extensive numerical experiments demonstrate that our methods achieve the desired temporal accuracy, measured by the manifold distance, while maintaining good mesh quality throughout the evolution. |
| title | High-order temporal parametric finite element methods for simulating solid-state dewetting |
| topic | Numerical Analysis Mathematical Physics 65M60, 65M12, 35K25 G.1.8; G.1.10 |
| url | https://arxiv.org/abs/2510.16493 |