Optimal control for Partial Differential Equations

In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control problems governed by elliptic and parabolic PDEs, implementing a steady and unsteady solver, using the Mlife library for Matlab. Finally, we apply the methods above to an inverse problem dealing with a problem of nuclear contamination.