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A Third-Order Weighted Essentially Non-Oscillatory Scheme in Optimal Control Problems Governed by Nonlinear Hyperbolic Conservation Laws

  • 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.

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Metadaten
Author:David Frenzel, Jens Lang
DOI:https://doi.org/https://doi.org/10.1007/s10589-021-00295-2
Document Type:Article
Language:English
Date of Publication (online):2021/02/27
Date of first Publication:2021/02/27
Release Date:2021/02/27
Volume:Computational Optimization and Applications
Issue:80
Page Number:20
First Page:301
Last Page:320
Subprojects:B01
Licence (German):License LogoCreative Commons - CC0 1.0 - Universell - Public Domain Dedication