An unconditionally energy stable and positive upwind DG scheme for the Keller-Segel model
arXiv:2209.10508 · doi:10.1007/s10915-023-02320-4
Abstract
The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and energy-dissipative discontinuous Galerkin scheme for the Keller-Segel model. This approach is based on the gradient-flow structure of the equations. In addition, we show some numerical experiments in accordance with the aforementioned properties of the discretization. The numerical results obtained emphasize the really good behaviour of the approximation in the case of chemotactic collapse, where very steep gradients appear.
arXiv comment27 pages, 21 figures, 4 tables
References in corpus (4)
- Improvements and generalizations of results concerning attraction-repulsion chemotaxis models
- A study of blow-ups in the Keller-Segel model of chemotaxis
- An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model
- Theoretical and numerical analysis for a hybrid tumor model with diffusion depending on vasculature