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

2025/04/16 by Li, Yifei
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2504.11926

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(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.

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