Abstract
This work aims to model the optimal control of dike heights. The control problem leads to so-called Hamilton-Jacobi-Bellman (HJB) variational inequalities, where the dike-increase and reinforcement times act as input quantities to the control problem. The HJB equations are solved numerically with an Essentially Non-Oscillatory (ENO) method. The ENO methodology is originally intended for hyperbolic conservation laws and is extended to deal with diffusion-type problems in this work. The method is applied to the dike optimisation of an island, for both deterministic and stochastic models for the economic growth.
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van der Pijl, S.P., Oosterlee, C.W. An ENO-Based Method for Second-Order Equations and Application to the Control of Dike Levels. J Sci Comput 50, 462–492 (2012). https://doi.org/10.1007/s10915-011-9493-3
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DOI: https://doi.org/10.1007/s10915-011-9493-3