An ENO-Based Method for Second-Order Equations and Application to the Control of Dike Levels

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 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.