A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model
Year: 2023
Type: preprint
Abstract: We study a finite volume scheme approximating a parabolic-elliptic Keller-Segel system with power law diffusion with exponent $γ\in [1,3]$ and periodic boundary conditions. We derive conditional a posteriori bounds for the error measured in the $L^\infty(0,T;H^1(Ω))$ 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 $γ$.
Source: arXiv (Cornell University)
Authors: Giesselmann, Jan, Kolbe, Niklas
Institutions: Technische Universität Darmstadt, RWTH Aachen University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4386794536