An optimal error bound for a finite element approximation of spatially extended predator-prey interaction model

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, 525–589 2000) 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, 641–667 2007). We also present some numerical experiments to illustrate the improved error bound.