Abstract
In this paper, we study a nonlinear in time finite element discretization of a spatially extended predator-prey interaction model. Assuming more regularity on the initial data and using the approach in Nochetto et al. (Commun. Pure Appl. Math.53, 525-5892000) for analyzing the time discretization error in the backward Euler method, we improve on the error bound derived in Garvie and Trenchea (Numer. Math.107, 641-6672007). We also present some numerical experiments to illustrate the improved error bound.