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Two-stage methods addressing continuous shortest path problems start localminimization from discrete shortest paths in a spatial graph. The convergenceof such hybrid methods to global minimizers hinges on the discretization errorinduced by restricting the discrete global optimization to the graph, withcorresponding implications on choosing an appropriate graph density. A primeexample is flight planning, i.e., the computation of optimal routes in view offlight time and fuel consumption under given weather conditions. Highlyefficient discrete shortest path algorithms exist and can be used directly forcomputing starting points for locally convergent optimal control methods. Wederive a priori and localized error bounds for the flight time of discretepaths relative to the optimal continuous trajectory, in terms of the graphdensity and the given wind field. These bounds allow designing graphs with anoptimal local connectivity structure. The properties of the bounds areillustrated on a set of benchmark problems. It turns out that localizationimproves the error bound by four orders of magnitude, but still leaves ampleopportunities for tighter error bounds by a posteriori estimators.

Error Bounds for Discrete-Continuous Shortest Path Problems with Application to Free Flight Trajectory Optimization