Solving an Elliptic Optimal Control Problem with BEM and FEM

n this paper, a constrained optimal control problem is considered where constraint is elliptic partial differential equations of second order together with the boundary condition of Dirichlet type. The main purpose is detecting an appropriate solution for control and state function by using boundary element method in order to discretized PDEs. In this way, first a quadratic objective, linear constraints optimization problem rewritten respected to main problem, next it can be solved numerically with the help of appropriate solution algorithms, which should exploit the structure of the problem, we solved it by generalized Newton’s method. Some numerical experiments obtained by using boundary element method (BEM) and finite element method (FEM) are given in the final section of this paper.