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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.11926 |
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| _version_ | 1866912522597040128 |
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| author | Li, Yifei |
| author_facet | Li, Yifei |
| contents | This paper presents a convergence analysis of the evolving surface finite element method (ESFEM) applied to the original Eyles-King-Styles model of tumour growth. The model consists of a Poisson equation in the bulk, a forced mean curvature flow on the surface, and a coupled velocity law between bulk and surface. Due to the non-trivial bulk-surface coupling, all previous analyses required an additional regularization term. By introducing a $H^{1/2}(Γ)$ energy estimates theory, we develop an essentially new theoretical framework that addresses the intrinsic bulk-surface coupling. Based on this framework, we provide the first rigorous convergence proof for the original model without regularization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of finite elements for the Eyles-King-Styles model of tumour growth Li, Yifei Numerical Analysis This paper presents a convergence analysis of the evolving surface finite element method (ESFEM) applied to the original Eyles-King-Styles model of tumour growth. The model consists of a Poisson equation in the bulk, a forced mean curvature flow on the surface, and a coupled velocity law between bulk and surface. Due to the non-trivial bulk-surface coupling, all previous analyses required an additional regularization term. By introducing a $H^{1/2}(Γ)$ energy estimates theory, we develop an essentially new theoretical framework that addresses the intrinsic bulk-surface coupling. Based on this framework, we provide the first rigorous convergence proof for the original model without regularization. |
| title | Convergence of finite elements for the Eyles-King-Styles model of tumour growth |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.11926 |