An Unconditionally Energy Stable and Positive Upwind DG Scheme for the Keller–Segel Model
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–...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::5de28cdc19066376e231bf722ec1a677 |
| Acceso en línea: | https://hdl.handle.net/11441/187091 https://doi.org/10.1007/s10915-023-02320-4 |
| Access Level: | acceso abierto |
| Palabra clave: | Keller–Segel equations Chemotaxis Discontinuous Galerkin Upwind scheme Positivity preserving Energy stability |
| Sumario: | 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. |
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