Artículo
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes
Autor/es | Guillén González, Francisco Manuel
Rodríguez Bellido, María Ángeles Rueda Gómez, Diego Armando |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2021-12-10 |
Fecha de depósito | 2022-06-30 |
Publicado en |
|
Resumen | We consider the following repulsive-productive chemotaxis model: find 0, the
cell density, and 0, the chemical concentration, satisfying
0 in 0
in 0
(1)
with 1 2 , a bounded domain ( 1 2 3), endowed with non-flux
boundary ... We consider the following repulsive-productive chemotaxis model: find 0, the cell density, and 0, the chemical concentration, satisfying 0 in 0 in 0 (1) with 1 2 , a bounded domain ( 1 2 3), endowed with non-flux boundary conditions. By using a regularization technique, we prove the existence of global in time weak solutions of (1) which is regular and unique for 1 2. Moreover, we propose two fully discrete Finite Element (FE) nonlinear schemes, the first one defined in the variables under structured meshes, and the second one by using the auxiliary variable and defined in general meshes. We prove some unconditional properties for both schemes, such as mass-conservation, solvability, energy-stability and approximated positivity. Finally, we compare the behavior of these schemes with respect to the classical FE backward Euler scheme throughout several numerical simulations and give some conclusions. |
Cita | Guillén González, F.M., Rodríguez Bellido, M.Á. y Rueda Gómez, D.A. (2021). A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes. Advances in computational mathematics, 47 (6), 87-1-87-38. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
A chemorepulsion model with ... | 4.370Mb | [PDF] | Ver/ | |