hN-adaptive spectral element discretization of optimal control problems for environmental applications

In this work, we propose an hN adaptive algorithm for optimal control problems whose space discretization is based on the spectral element method. We focus on a special class of problems described by quadratic cost functional and linear advection-diffusion state equation. This model has been employed to forecast and suitably reduce, by an optimization process, the pollutant concentration in air on a specic area of interest. Moreover, a local adaptive algorithm is employed to achieve a desired accuracy on the cost functional by reducing the computational cost of the problem.