Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/287360 
Year of Publication: 
2021
Citation: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 80 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2021 [Pages:] 301-320
Publisher: 
Springer US, New York, NY
Abstract: 
The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock is present, they still have uniform high-order accuracy right up to the shock location. In this paper, we propose a novel third-order numerical method for solving optimal control problems subject to scalar nonlinear hyperbolic conservation laws. It is based on the first-disretize-then-optimize approach and combines a discrete adjoint WENO scheme of third order with the classical strong stability preserving three-stage third-order Runge–Kutta method SSPRK3. We analyze its approximation properties and apply it to optimal control problems of tracking-type with non-smooth target states. Comparisons to common first-order methods such as the Lax–Friedrichs and Engquist–Osher method show its great potential to achieve a higher accuracy along with good resolution around discontinuities.
Subjects: 
Nonlinear optimal control
Discrete adjoints
Hyperbolic conservation laws
WENO schemes
Strong stability preserving Runge–Kutta methods
JEL: 
H05
M25
L06
M22
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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