TY - JOUR A1 - Ulbrich, Stefan A1 - Schmitt, Johann Michael A1 - Schäfer Aguilar, Paloma A1 - Moos, Michael T1 - On the numerical discretization of optimal control problems for conservation laws N2 - We analyze the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal control problems governed by entropy solutions of conservation laws. The difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and discontinuous end data. We derive the discrete adjoint scheme for monotone difference schemes in conservation form. It is known that convergence of the discrete adjoint can only be expected if the numerical scheme has viscosity of order O(h^\alpha) with appropriate 0 < \alpha < 1, which leads to quite viscous shock profiles. We show that by a slight modification of the end data of the discrete adjoint scheme convergence to the correct reversible solution can be obtained also for numerical schemes with viscosity of order O(h) and with sharp shock resolution. The theoretical findings are confirmed by numerical results. Y1 - 2019 ER -