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A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model

Submission Status:under review
  • 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.

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Author:Jan Giesselmann, Niklas Kolbe
Document Type:Preprint
Date of Publication (online):2024/02/13
Release Date:2024/02/13
Tag:Keller-Segel; a posteriori error analysis; chemotaxis;; finite volume scheme; nonlinear diffusion
Institutes:Technische Universität Darmstadt
RWTH Aachen University
Licence (German):License LogoCreative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International