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

Artikel

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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Journal: Computational Optimization and Applications ; ISSN: 1573-2894 ; Volume: 80 ; Year: 2021 ; Issue: 1 ; Pages: 301-320 ; New York, NY: Springer US

Klassifikation und Themen

• Klassifikation: Mathematik
• Thema: Nonlinear optimal control ; Discrete adjoints ; Hyperbolic conservation laws ; WENO schemes ; Strong stability preserving Runge–Kutta methods

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Frenzel, David ; Lang, Jens
• Ereignis: Veröffentlichung
• (wer): Springer US
• (wo): New York, NY
• (wann): 2021

Weitere Informationen

• DOI: doi:10.1007/s10589-021-00295-2
• Letzte Aktualisierung: 10.03.2025, 11:44 MEZ