Numerical analysis of a three-species chemotaxis model

Abstract A reaction–diffusion system is formulated to describe three interacting species within the Hastings–Powell (HP) food chain structure with chemotaxis produced by three chemicals. We construct a finite volume (FV) scheme for this system, and in combination with the non-negativity and a priori estimates for the discrete solution, the existence of a discrete solution of the FV scheme is proven. It is shown that the scheme converges to the corresponding weak solution of the model. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space–time L 1 compactness argument. Finally, numerical tests illustrate the model and the behavior of the FV scheme.