Finite element approximation of a Keller-Segel model with additional self- and cross-diffusion terms and a logistic source

A fully finite element approximation of the Keller-Segel model, including self- and cross-diffusion terms and a logistic source, has been considered. The existence of a fully finite element approximation of the Keller-Segel model, some stability bounds of the solution and the convergence of the approximated solution have been shown. As a result, the existence of a solution to the nonlinear Keller-Segel model in R-d, d <= 3 has been demonstrated. Moreover, an iterative approach to solving the resulted nonlinear discrete system has been introduced. Finally, some numerical results have been shown. (C) 2021 Elsevier B.V. All rights reserved.