The project provides a detailed mathematical analysis and consistent numerical discretization of optimal control problems for networks/systems of hyperbolic balance laws with state constraints as they arise for unsteady PDE models for gas networks. The results are used for the computation of convergent discrete gradients within derivative-based optimization methods. To this end, numerical approximations for a class of adjoint and sensitivity equations are studied, using the discretize-then-optimize as well as the optimize-then-discretize approach. In a further step, the project will consider higher order schemes and derive a priori error estimators for optimal control of entropy solutions.
DFG Programme
CRC/Transregios
