# Finite Element Method for Optimal Control of Elliptic Partial Differential Equations

## Ajeeb ur Rehman Junejo

**April 26, 2013, 4 p.m. S2 059**

In this presentation numerical methods of optimal control of elliptic partial differential equations (EPDE) will be discussed, i.e, the problems which consisting on minimizing a cost functional subject to EPDE constrains will be discussed. In this talk the goal is to use FEniCS software to determine the state and control which minimize the corresponding cost functional, for this purpose we used numerical method based on an indirect approach, which means first derive the optimality system then solve numerically.

In this work optimality system is derived by two ways, first way is based on Lagrange's method and other by reduced functional. Discretization of Optimality system of Optimal control for (EPDE) by finite element method is considered. Computation and comparison of exact and approximate solutions by two dierent ways, computation of error analysis by differnt ways and computation of convergence rate by using FEniCS software also will be presented.