631	RWTH Publication No: 975677        2023
TITLE	A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model
AUTHORS	Jan Giesselmann, Niklas Kolbe
ABSTRACT	We study a finite volume scheme approximating a parabolic-elliptic Keller-Segel system with power law diffusion with exponent γ ∈ [1, 3] and periodic boundary conditions. We derive conditional a posteriori bounds for the error measured in the L∞(0, T; H1(Ω)) norm for the chemoattractant and by a quasi-norm-like quantity for the density. These results are based on stability estimates and suitable conforming reconstructions of the numerical solution. We perform numerical experiments showing that our error bounds are linear in mesh width and elucidating the behaviour of the error estimator under changes of γ .
KEYWORDS	Keller-Segel; chemotaxis; nonlinear diffusion; finite volume scheme; a posteriori error analysis