• Corpus ID: 239024400

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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