Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms
Numerical Analysis
2020-01-28 v1 Numerical Analysis
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 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.
Keywords
Cite
@article{arxiv.2001.09544,
title = {Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms},
author = {Esther S. Daus and Ansgar Jüngel and Antoine Zurek},
journal= {arXiv preprint arXiv:2001.09544},
year = {2020}
}