Publications in Scientific Journals:
M. Bessemoulin-Chatard, A. Jüngel:
"A finite volume scheme for a Keller-Segel model with additional cross-diffusion";
IMA Journal of Applied Mathematics,
A finite volume scheme for the (Patlak-) Keller-Segel model in two space dimensions with an additional
cross-diffusion term in the elliptic equation for the chemical signal is analysed. The main feature of the
model is that there exists a new entropy functional yielding gradient estimates for the cell density and
chemical concentration. The main features of the numerical scheme are positivity preservation, mass
conservation, entropy stability and-under additional assumptions-entropy dissipation. The existence
of a discrete solution and its numerical convergence to the continuous solution is proved. Furthermore,
temporal decay rates for convergence of the discrete solution to the homogeneous steady state is shown
using a new discrete logarithmic Sobolev inequality. Numerical examples point out that the solutions
exhibit intermediate states and that there exist nonhomogeneous stationary solutions with a finite cell
density peak at the domain boundary.
Siehe englisches Abstract.
finite volume method; chemotaxis; cross-diffusion model
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Created from the Publication Database of the Vienna University of Technology.