Mathematical and numerical analysis for Predator-prey system in a polluted environment

In this paper, we prove existence results for a Predator-prey system in a polluted environment. The existence result is proved by the Schauder fixed-point theorem. Moreover, we construct a combined finite volume finite element scheme to our model, we establish existence of discrete solutions to this scheme, and show that it converges to a weak solution. The convergence proof is based on deriving series of a priori estimates and using a general Lp compactness criterion. Finally we give some numerical examples.