Analysis of a fully discrete approximation for the classical Keller–Segel model: Lower and a priori bounds

This paper is devoted to constructing approximate solutions for the classical Keller–Segel model governing chemotaxis . It consists of a system nonlinear parabolic equations, where unknowns are average density cells (or organisms), which conserved variable, and chemoattractant. The numerical proposal made up crude finite element method together with mass lumping technique semi-implicit Euler time integration. resulting scheme turns out be linear decouples computation variables. keep lower bounds – positivity cell nonnegativity chemoattractant density–, bounded in L 1 ( Ω ) -norm, satisfy discrete energy law, have priori estimates. latter achieved by means Moser–Trudinger inequality. As far as we know, our first one that can encountered literature dealing all previously mentioned properties at same time. Furthermore, some examples carried support complement theoretical results.