An ENO-based method for second-order equations and application to the control of dike levels

S. P. Van Der Pijl; C. W. Oosterlee

doi:10.1007/s10915-011-9493-3

An ENO-based method for second-order equations and application to the control of dike levels

S. P. Van Der Pijl, C. W. Oosterlee^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	462-492
Number of pages	31
Journal	Journal of Scientific Computing
Volume	50
Issue number	2
DOIs	https://doi.org/10.1007/s10915-011-9493-3
Publication status	Published - Feb 2012
Externally published	Yes

Keywords

Dike increase against flooding
ENO scheme for diffusion
Hamilton-Jacobi-Bellman equations
Impulsive control

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1007/s10915-011-9493-3

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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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AU - Oosterlee, C. W.

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N2 - 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.

AB - 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.

KW - Dike increase against flooding

KW - ENO scheme for diffusion

KW - Hamilton-Jacobi-Bellman equations

KW - Impulsive control

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JO - Journal of Scientific Computing

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ER -

An ENO-based method for second-order equations and application to the control of dike levels

Abstract

Keywords

UN SDGs

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