**Víctor Hernández-Santamaría** earned his Ph.D. degree in the department of automatic control in CINVESTAV (Mexico), under the supervision of Luz de Teresa (Instituto de Matemáticas, UNAM, México) and Alexander Poznyak (CINVESTAV). His research interests are related to control problems for coupled parabolic equations, especially, those arising in the insensitizing control and hierarchic control problems, both from a theoretical and numerical point of view. He holded a Postdoctoral position at the ERC DyCon Advanced Grant project under the supervision of Prof. Enrique Zuazua.

#### Author's contribution:

#### Finite Element approximation of the one-dimensional fractional Laplacian

We describe a FE method for the approximation of the one-dimensional fractional Laplacian $(-d_x^2)^s$ on a uniform mesh discretizing the symmetric interval $(-L,L)$, $L>0$.

#### Optimal Control of the Poisson Equation with OpenFOAM

In this tutorial, we show how to use the C++ library OpenFOAM (Open Field Operation and Manipulation) in order to solve control problems for partial differential equations (PDE).

#### Averaged Control

In this work, we address the optimal control of parameter-dependent systems.

#### Greedy optimal control for elliptic problems and its application to turnpike problems

Turnpike theory and greedy algorithms, applied to the steady-state elliptic control problem, are combined to obtain a greedy approximation of parabolic optimal control problems, independent of the initial data