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Main Author: Li, Yifei
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2504.11926
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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