8331 2023 eng 830 856 198 article 0 -- -- -- Flight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods. Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories. Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators. Journal of Optimization Theory and Applications 10.1007/s10957-023-02264-7 yes publish 2023-06-19 Ralf Borndörfer Martin Weiser Fabian Danecker Martin Weiser Borndörfer, Ralf Weiser, Martin Modeling and Simulation of Complex Processes Network Optimization MathPlus-AA3-3 https://opus4.kobv.de/opus4-zib/files/8331/article.pdf