Adjoint IMEX-based schemes for control problems governed by hyperbolic conservation laws

Authors:
Mapundi K. Banda;Michael Herty
Affiliations:
Faculty of Science, University of the Witwatersrand, Wits, South Africa 2050;RWTH Aachen University, Aachen, Germany 52056
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

Starting from relaxation schemes for hyperbolic conservation laws we derive continuous and discrete schemes for optimization problems subject to nonlinear, scalar hyperbolic conservation laws. We discuss properties of first- and second-order discrete schemes and show their relations to existing results. In particular, we introduce first and second-order relaxation and relaxed schemes for both adjoint and forward equations. We give numerical results including tracking type problems with non-smooth desired states.