Optimal solution of a diffusion equation with a discrete source term

Abstract

In this paper we study the numerical behavior of a diffusion equation with a discrete control source term. The equation is discretized in space by finite differences and in time by an implicit scheme. The control variables are calculated in order to minimize an objective function, taking into account some restrictions. We define two strategies to obtain the optimal solution and present some numerical results in a context of a model that describes the oxygen concentration in a single chamber microbial fuel cell.