Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
This work is devoted to the study of a fully discrete scheme for a repulsive chemotaxis with quadratic production model. By following the ideas presented in Guillén-González et al. (2020), we introduce an auxiliary variable (the gradient of the chemical concentration), and prove that the correspondi...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::a3b9234313c00c4cad2f035b8ccae850 |
| Acceso en línea: | https://hdl.handle.net/11441/186555 https://doi.org/10.1016/j.camwa.2020.04.010 |
| Access Level: | acceso abierto |
| Palabra clave: | Chemorepulsion–production model Fully discrete scheme Finite element method Energy-stability Convergence Error estimates |
| Sumario: | This work is devoted to the study of a fully discrete scheme for a repulsive chemotaxis with quadratic production model. By following the ideas presented in Guillén-González et al. (2020), we introduce an auxiliary variable (the gradient of the chemical concentration), and prove that the corresponding Finite Element (FE) backward Euler scheme is conservative and unconditionally energy-stable. Additionally, we also study some properties like solvability, a priori estimates, convergence towards weak solutions and error estimates. On the other hand, we propose two linear iterative methods to approach the nonlinear scheme: an energy-stable Picard method and Newton’s method. We prove solvability and convergence of both methods towards the nonlinear scheme. Finally, we provide some numerical results in agreement with our theoretical analysis with respect to the error estimates. |
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