Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
A Weighted Essentially Nonoscillatory, Large Time-Step Scheme for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
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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.