论文标题
用于生物膜的退化式交叉扩散系统的有限体积方案的收敛
Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms
论文作者
论文摘要
通过利用其正式的梯度流结构来分析一种跨扩散系统建模生物膜增长的隐式欧拉有限体积方案。数值方案基于两点通量近似，该近似保留了连续模型的熵结构。假设相等的扩散性，证明了对该方案及其收敛的非负和有限解决方案的存在。最后，我们通过数值实验在一个和两个空间维度中补充了研究。
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.
