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A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws

Frenzel, David ; Lang, Jens (2024)
A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws.
In: Computational Optimization and Applications, 2021, 80 (1)
doi: 10.26083/tuprints-00023518
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws
Language: English
Date: 10 December 2024
Place of Publication: Darmstadt
Year of primary publication: September 2021
Place of primary publication: New York
Publisher: Springer Science
Journal or Publication Title: Computational Optimization and Applications
Volume of the journal: 80
Issue Number: 1
DOI: 10.26083/tuprints-00023518
Corresponding Links:
Origin: Secondary publication DeepGreen
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.

Uncontrolled Keywords: Nonlinear optimal control, Discrete adjoints, Hyperbolic conservation laws, WENO schemes, Strong stability preserving Runge–Kutta methods
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-235183
Additional Information:

Mathematics Subject Classifcation 34H05 · 49M25 · 65L06 · 65M22

Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 10 Dec 2024 12:53
Last Modified: 10 Dec 2024 12:53
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/23518
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