Finite volume method for a Keller-Segel problem

In this paper, we are interested in the numerical simulation of the mathematical model of Keller-Segel Elliptic-Parabolic problem using finite volume scheme. The finite volume scheme is applied to the elliptic-parabolic model’s problem and we have shown under certain assumptions, the existence of a unique and positive approximate solution. Moreover, under adequate regularity assumption of the exact solution, the finite volume scheme is the first order accurate. A good agreement between our numerical simulation and the theoretical results has been obtained.