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On the numerical behavior of a chemotaxis model with linear production term. (English) Zbl 1452.92008

Ortegon Gallego, Francisco (ed.) et al., Recent advances in pure and applied mathematics. Based on contributions presented at the Second Joint Meeting Spain-Brazil in Mathematics, Cádiz, Spain, December 11–14, 2018. Cham: Springer. RSME Springer Ser. 4, 61-73 (2020).
The authors study a system of two parabolic equations modelling chemorepulsion with power type production term. Summarizing recent reports on the numerical analysis of those systems, they discuss properties of three versions of finite element methods applicable to an initial-boundary value problem in two dimensional domains, with a particular stress on (classical) linear production term in the evolution equation for the diffusion of chemicals.
For the entire collection see [Zbl 1445.37001].

MSC:

92C17 Cell movement (chemotaxis, etc.)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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