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arXiv · 2504.11926

Convergence of finite elements for the Eyles-King-Styles model of tumour growth

Yifei Li
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Abstract

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 $H^{1/2}(\Gamma)$ 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.

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Yifei Li. 2025-04-16. Convergence of finite elements for the Eyles-King-Styles model of tumour growth. https://arxiv.org/abs/2504.11926

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