ISBN 9783843944540

978-3-8439-4454-0, Reihe Mathematik

David Frenzel
Weighted Essentially Non-Oscillatory Schemes in Optimal Control Problems Governed by Nonlinear Hyperbolic Conservation Laws

177 Seiten, Dissertation Technische Universität Darmstadt (2020), Hardcover, B5

Zusammenfassung / Abstract

In this thesis numerical methods for solving optimal control problems subject to scalar nonlinear hyperbolic conservation laws are studied. Based on Weighted Essentially Non-Oscillatory (WENO) schemes, discrete adjoint WENO methods for the resolution of the adjoint equation are derived. We analyze the approximation order of adjoint WENO schemes and present numerical examples for the approximation properties of discrete adjoints as well as optimal control problems of tracking-type with nonsmooth desired states. We compare the numerical results to the common first-order methods such as the Lax-Friedrichs and the Engquist-Osher method.