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On the consistency of Runge--Kutta methods up to order three applied to the optimal control of scalar conservation laws

  • Higher-order Runge-Kutta (RK) time discretization methods for the optimal control of scalar conservation laws are analyzed and numerically tested. The hyperbolic nature of the state system introduces specific requirements on discretization schemes such that the discrete adjoint states associated with the control problem converge as well. Moreover, conditions on the RK-coefficients are derived that coincide with those characterizing strong stability preserving Runge-Kutta methods. As a consequence, the optimal order for the adjoint state is limited, e.g., to two even in the case where the conservation law is discretized by a third-order method. Finally, numerical tests for controlling Burgers equation validate the theoretical results.
Metadaten
Author:Michael Hintermüller, Nikolai Strogies
DOI:https://doi.org/10.20347/WIAS.PREPRINT.2442
Parent Title (English):Numerical Analysis and Optimization
Document Type:Article
Language:English
Date of Publication (online):2017/10/31
Date of first Publication:2017/10/31
Release Date:2017/10/31
First Page:119
Last Page:154
Institutes:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B02