Many technical processes are described by partial differential equations. Here, it is important to optimize these processes. This leads to optimization problems in an infinite-dimensional setting.
As model problem, consider the minimization of a functional Despite its simple structure, this problem offers many difficulties and challenges. Due to the non-linear elliptic equation this optimisation problem becomes non-convex.
If one has computed solutions y_h and u_h of discretized versions of this problem, the question arises Due to the inherent non-convexity of the optimization problem, this question by far non-trivial. The project want to give answers to this question with information that is computable from the numerical solution. The methods, which will be applied, are based on techniques from optimal control, finite element methods, and eigenvalue computations.