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 |
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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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