Error analysis of a backward euler positive preserving stabilized scheme for a chemotaxis system
Abstract
For a Keller–Segel model for chemotaxis in two spatial dimensions, we consider a modification of a positivity-preserving fully discrete scheme using a local extremum diminishing flux limiter. We discretize space using piecewise linear finite elements on a quasiuniform triangulation of acute type and time by the backward Euler method. We assume that initial data are sufficiently small in order not to have a blow-up of the solution. Under appropriate assumptions on the regularity of the exact solution and the time step parameter, we show existence of the fully discrete approximation and derive error bounds in L 2 for the cell density and H 1 for the chemical concentration. We also present numerical experiments to illustrate the theoretical results.
Fields of Study & Subjects
Mathematical Biology Tumor Growth
MRI in cancer diagnosis
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- ESAIM Mathematical Modelling and Numerical Analysis
- Volume
- 60
- Issue
- 4
- Pages
- 1601–1634
- Publication date
- 20 April 2026
- Language
- EN