A Finite Element Technique to the Optimal Control of Two Dimensional Diffusion Equations

Abstract

This paper dealt with the study of the optimal control (u(x,t)) and optimal state (z(x,t)) for two dimensional diffusion equations using finite element method (FEM). The finite element method is a very powerful tool for getting numerical solution of a wide range of engineering problems. The optimal control profile ue and the optimal state profile ze against the number of element e of the two dimensional diffusion solutions with varying space dimension n are obtained. It was discovered that the nodal temperature shows cooling effect from the left to the right side of the rod, and subsequently the output decreases. It is symmetric in nature.