Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms

Esther Daus (1) , Ansgar Jüngel (2) , Antoine Zurek (1)

1 Institute for Analysis and Scientific Computing [Wien]
2 TU Wien - Vienna University of Technology = Technische Universität Wien

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.

Domaines: Analyse numérique [math.NA]

Esther Daus, Ansgar Jüngel, Antoine Zurek. Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms. 2020. ⟨hal-02455755v1⟩