Artículo
Analysis of a fully discrete approximation for the classical Keller–Segel model: Lower and a priori bounds
Autor/es | Gutiérrez Santacreu, Juan Vicente
Rodríguez Galván, José Rafael |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2021 |
Fecha de depósito | 2022-06-22 |
Publicado en |
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Resumen | This paper is devoted to constructing approximate solutions for the classical Keller–Segel model governing chemotaxis. It consists of a system of nonlinear parabolic equations, where the unknowns are the average density ... This paper is devoted to constructing approximate solutions for the classical Keller–Segel model governing chemotaxis. It consists of a system of nonlinear parabolic equations, where the unknowns are the average density of cells (or organisms), which is a conserved variable, and the average density of chemoattractant. The numerical proposal is made up of a crude finite element method together with a mass lumping technique and a semi-implicit Euler time integration. The resulting scheme turns out to be linear and decouples the computation of variables. The approximate solutions keep lower bounds – positivity for the cell density and nonnegativity for the chemoattractant density–, are bounded in the -norm, satisfy a discrete energy law, and have a priori energy estimates. The latter is achieved by means of a discrete Moser–Trudinger inequality. As far as we know, our numerical method is the first one that can be encountered in the literature dealing with all of the previously mentioned properties at the same time. Furthermore, some numerical examples are carried out to support and complement the theoretical results. |
Agencias financiadoras | Ministerio de Ciencia e Innovación (MICIN). España |
Identificador del proyecto | PGC2018-098308-B-I00 |
Cita | Gutiérrez Santacreu, J.V. y Rodríguez Galván, J.R. (2021). Analysis of a fully discrete approximation for the classical Keller–Segel model: Lower and a priori bounds. Computers and Mathematics with Applications, 85 (March 2021), 69-81. |
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