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

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-08-08 DOI:10.1515/cmam-2023-0009

Ansgar Jüngel, Martin Vetter

引用次数: 0

Abstract

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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种群交叉扩散系统的收敛熵耗散BDF2有限体积格式

摘要研究了一类非线性交叉扩散系统的二阶后向微分有限体积离散化问题。该数值格式保持了Rao熵结构和质量守恒。证明了离散解的存在唯一性及其大时性，并证明了该方案的收敛性。该证明基于BDF2格式的g稳定性，该格式提供了二次Rao熵的不等式，因此适合先验估计。新奇之处在于将这个不等式扩展到系统情况。一些一维和二维空间的数值实验证明了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.