Abstract
In this contribution we propose an optimally stable ultraweak Petrov-Galerkin variational formulation and subsequent discretization for stationary reactive transport problems. The discretization is exclusively based on the choice of discrete approximate test spaces, while the trial space is a priori infinite dimensional. The solution in the trial space or even only functional evaluations of the solution are obtained in a post-processing step. We detail the theoretical framework and demonstrate its usage in a numerical experiment that is motivated from modeling of catalytic filters.
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Notes
- 1.
We restrict to divergence free velocities. However, non-divergence free fields may be considered as well.
- 2.
References
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Acknowledgements
The authors acknowledge funding by the BMBF under contract 05M20PMA and by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy EXC 2044 390685587, Mathematics Münster: Dynamics—Geometry—Structure.
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Renelt, L., Engwer, C., Ohlberger, M. (2023). An Optimally Stable Approximation of Reactive Transport Using Discrete Test and Infinite Trial Spaces. In: Franck, E., Fuhrmann, J., Michel-Dansac, V., Navoret, L. (eds) Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems. FVCA 2023. Springer Proceedings in Mathematics & Statistics, vol 433. Springer, Cham. https://doi.org/10.1007/978-3-031-40860-1_30
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DOI: https://doi.org/10.1007/978-3-031-40860-1_30
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