退化奇异交叉扩散生物膜方程组有限体积格式的收敛性
Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms
摘要：
利用欧拉有限体积隐式格式的形式梯度流结构，分析了模拟生物膜生长的交叉扩散系统。数值方案是基于两点通量近似，保持连续模型的熵结构。在等扩散系数条件下，证明了该格式非负有界解的存在性及其收敛性。最后，我们补充的研究，在一个和两个空间维度的数值实验。
英文摘要：
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 nonnegative 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.
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