Adjoint IMEX-based schemes for control problems governed by hyperbolic conservation laws |
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| Authors: | Mapundi K Banda Michael Herty |
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| Affiliation: | (1) Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA;(2) Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA 94305, USA |
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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. |
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