| Issue |
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
|
|
|---|---|---|
| Page(s) | 517 - 540 | |
| DOI | https://doi.org/10.1051/m2an/2026012 | |
| Published online | 24 March 2026 | |
Numerical analysis of a semi-implicit Euler scheme for the Keller-Segel model
1
School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China
2
Laboratoire Paul Painlevé UMR 8524 U-Lille CNRS et INRIA, Lille 59000, France
3
School of Mathematical Science, Eastern Institute of Technology, Ningbo, Zhejiang 315200, China
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
7
February
2025
Accepted:
27
January
2026
Abstract
We study the properties of a semi-implicit Euler scheme widely used for time discretization of Keller-Segel equations in both parabolic-elliptic and parabolic-parabolic forms. We assume the initial mass of the cell density is sufficiently small to ensure that solutions of the continuous Keller-Segel equations exist globally in time. We prove that this linear, decoupled, first-order scheme preserves key properties of the Keller-Segel model at the semi-discrete level, including mass conservation, positivity preservation, and energy dissipation. We also establish optimal error estimates in Lp-norm (1 < p < ∞) for the scheme.
Mathematics Subject Classification: 92C17 / 65M12 / 35K20 / 35B09
Key words: Keller-Segel equations / mass conservation / positivity preserving / energy dissipation / error estimates
© The authors. Published by EDP Sciences, SMAI 2026
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