Abstract
This paper examines a finite element method for the chemotaxis-growth model with indirect attractant production and logistic source. To begin, we propose a regularized problem of the truncated problem. We then obtain some a priori estimates of regularized solutions that are independent of the regularization parameter using a well-defined entropy inequality for the regularized problem. Additionally, we offer an efficient fully discrete finite element approximation of the regularized problem. A fixed point theorem is then used to prove that the approximate solutions exist. A discrete entropy inequality is also proposed for fully discrete finite element problems, as well as some stability bounds. We also investigate the convergence of the fully discrete problem.
Disclosure statement
No potential conflict of interest was reported by the author(s).