一类群体交叉扩散系统的收敛熵耗散BDF2有限体积格式

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-01-09 DOI:10.48550/arXiv.2301.03200

A. Jüngel, M. Vetter

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引用次数: 0

摘要

摘要研究了种群动力学中非线性交叉扩散系统的二阶后向微分公式（BDF2）有限体积离散化问题。该数值格式保持了Rao熵结构并保持了质量，证明了离散解的存在性、唯一性及其大时间行为以及格式的收敛性。这些证明是基于BDF2格式的G-稳定性，它为二次Rao熵提供了一个不等式，从而提供了合适的先验估计。新颖之处在于将这种不等式扩展到系统情况。在一维和二维空间中的一些数值实验强调了理论结果。

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A Convergent Entropy-Dissipating BDF2 Finite-Volume Scheme for a Population Cross-Diffusion System

Abstract A second-order backward differentiation formula (BDF2) finite-volume discretization for a nonlinear cross-diffusion system arising in population dynamics is studied. The numerical scheme preserves the Rao entropy structure and conserves the mass. The existence and uniqueness of discrete solutions and their large-time behavior as well as the convergence of the scheme are proved. The proofs are based on the G-stability of the BDF2 scheme, which provides an inequality for the quadratic Rao entropy and hence suitable a priori estimates. The novelty is the extension of this inequality to the system case. Some numerical experiments in one and two space dimensions underline the theoretical results.

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.