Abstract
In this proceeding, we present model adaptation for hyperbolic balance laws based on a posteriori error estimates. The model adaptation is carried out by decomposing the computational domain and choosing to solve either the full system or a simpler reduced system. The decision is made based on error estimates constructed employing the relative entropy framework which allows us to bound the difference between the numerical solution to the reduced system and the exact solution to the full system. Furthermore, the use of surrogate fluxes in the simple model constructed by machine learning is proposed to further reduce the computational expenses.
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Acknowledgements
This research is supported by the German Research Foundation (DFG) grant GI1131/1-1: Dynamical, spatially heterogeneous model adaptation in compressible flows.
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Giesselmann, J., Joshi, H. (2020). Model Adaptation of Balance Laws Based on A Posteriori Error Estimates and Surrogate Fluxes. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_34
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DOI: https://doi.org/10.1007/978-3-030-43651-3_34
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