**Prof. Nicolas R. Gauger is a professor in the Computational Mathematics Group,Department of Mathematics and Center for Computational Engineering Science, RWTH. He will be hosted by Prof. Qiqi Wang until the end of August, 2014.**

The one-shot method has proven to be very efficient in optimization with steady partial differential

equations (PDEs). In this approach, the necessary optimality conditions, resulting in

the state, the adjoint, and the design equations, are solved simultaneously. Applications of the

one-shot method in the field of aerodynamic shape optimization with steady Navier-Stokes

equations have shown, that the computational cost for an optimization, measured in runtime

as well as iteration counts, is only 2 to 8 times the cost of a single simulation of the governing

PDE. In this talk, we present a framework for applying the one-shot approach also to optimization

and control problems with the unsteady Navier-Stokes equations. Straight forward

applications of the one-shot method to unsteady problems have shown, that its efficiency depends

on the resolution of the physical time domain. In order to dissolve this dependency, we

consider an unsteady model problem and investigate an adaptive time scaling approach, which

yields the same efficiency as observed for steady problems.