Abstract

An implicit Euler finite-volume scheme for a cross-diffusion system modeling biofilm growth is analyzed by exploiting its formal gradient-flow structure. The numerical scheme is based on a two-point flux approximation that preserves the entropy structure of the continuous model. Assuming equal diffusivities the existence of non-negative and bounded solutions to the scheme and its convergence are proved. Finally, we supplement the study by numerical experiments in one and two space dimensions.

中文翻译：

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生物膜的退化奇异交叉扩散系统的有限体积格式的收敛性

摘要

通过利用其形式梯度流结构，分析了用于建模生物膜生长的交叉扩散系统的隐式Euler有限体积方案。数值方案基于两点通量近似值，该近似值保留了连续模型的熵结构。假设扩散率相等，则证明了该方案的非负有界解的存在性及其收敛性。最后，我们通过一维和二维空间的数值实验对研究进行补充。