  On the one hand, Sobolev gradient smoothing can considerably improve the
performance of aerodynamic shape optimization and prevent issues with
regularity. On the other hand, Sobolev smoothing can also be interpreted as an
approximation for the shape Hessian. This paper demonstrates, how Sobolev
smoothing, interpreted as a shape Hessian approximation, offers considerable
benefits, although the parameterization is smooth in itself already. Such an
approach is especially beneficial in the context of simultaneous analysis and
design, where we deal with inexact flow and adjoint solutions, also called One
Shot optimization. Furthermore, the incorporation of the parameterization
allows for direct application to engineering test cases, where shapes are
always described by a CAD model. The new methodology presented in this paper is
used for reference test cases from aerodynamic shape optimization and
performance improvements in comparison to a classical Quasi-Newton scheme are
shown.
