标题： 肿瘤生长的Eyles-King-Styles模型的有限元收敛性 显示英文标题

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

摘要： 本文提出了对肿瘤生长原始Eyles-King-Styles模型应用的演化曲面有限元方法（ESFEM）的收敛性分析。 该模型包括体内的泊松方程、表面上的强迫平均曲率流，以及体和表面之间的耦合速度定律。 由于非平凡的体-表面耦合，所有以前的分析——这些分析都仅依赖于能量估计方法——都需要一个额外的正则化项。 通过采用$\widehat{H}^{3/2}$理论和多重线性形式，我们建立了一个本质上新的理论框架，使得可以将偏微分方程正则性理论应用于稳定性分析。 基于此框架，我们提供了无需正则化的原始模型的第一个严格收敛证明。 显示英文摘要

摘要： This paper presents a convergence analysis of evolving surface finite element methods (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 -- which exclusively relied on energy-estimate based approaches -- required an additional regularization term. By adopting the $\widehat{H}^{3/2}$ theory and the multilinear forms, we develop an essentially new theoretical framework that enables the application of PDE regularity theory to stability analysis. Based on this framework, we provide the first rigorous convergence proof for the original model without regularization.