# Optimal control using flux potentials: A way to construct bound-preserving finite element schemes for conservation laws

@article{Ruppenthal2021OptimalCU, title={Optimal control using flux potentials: A way to construct bound-preserving finite element schemes for conservation laws}, author={Falko Ruppenthal and Dmitri Kuzmin}, journal={ArXiv}, year={2021}, volume={abs/2110.09912} }

To ensure preservation of local or global bounds for numerical solutions of conservation laws, we constrain a baseline finite element discretization using optimization-based (OB) flux correction. The main novelty of the proposed methodology lies in the use of flux potentials as control variables and targets of inequality-constrained optimization problems for numerical fluxes. In contrast to optimal control via general source terms, the discrete conservation property of flux-corrected finite…

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