Cahn-Hilliard-Brinkman-Ohta-Kawasaki肿瘤生长模型的完全解耦不连续伽辽金近似和最优误差估计

IF 1.9 3区 数学 Q2 Mathematics
Guang‐an Zou, Bo Wang, X. Yang
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引用次数: 3

摘要

摘要在本文中,我们考虑Cahn-Hilliard-Brinkman-Ohta-Kawasaki肿瘤生长系统,该系统耦合了多孔介质中的Brinkman流动方程和具有非局部Ohta-Kawasaki项的Cahn-Hilliard型方程。首先基于时间离散中的解耦稳定能量分解方法和隐显欧拉方法构造了一个完全解耦的不连续Galerkin方法,并严格证明了其无条件能量稳定性。进一步得到了肿瘤间质液压力的最佳误差估计。数值结果验证了所提数值格式的有效性,并验证了理论结果。最后,我们将该方案应用于基于患者特异性磁共振成像的脑肿瘤进化模拟,得到的计算结果表明,所提出的数值模型和方案能够提供真实的计算和预测,从而深入了解脑肿瘤的生长机制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A fully-decoupled discontinuous Galerkin approximation and optimal error estimate of the Cahn-Hilliard-Brinkman-Ohta-Kawasaki tumor growth model
Abstract. In this article, we consider the Cahn-Hilliard-Brinkman-Ohta-Kawasaki tumor growth system, which couples the Brinkman flow equations in the porous medium and the Cahn-Hilliard type equation with the nonlocal Ohta-Kawasaki term. We first construct a fully-decoupled discontinuous Galerkin method based on a decoupled, stabilized energy factorization approach and implicit-explicit Euler method in the time discretization, and strictly prove its unconditional energy stability. The optimal error estimate for the tumor interstitial fluid pressure is further obtained. Numerical results are also carried out to demonstrate the effectiveness of the proposed numerical scheme and verify the theoretical results. Finally, we apply the scheme to simulate the evolution of brain tumors based on patient-specific magnetic resonance imaging, and the obtained computational results show that the proposed numerical model and scheme can provide realistic calculations and predictions, thus providing an in-depth understanding of the mechanism of brain tumor growth.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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