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Combining reciprocity gap method and state estimator for source identification in an advection diffusion equation
Antoine Tonnoir1
1 LMI INSA Rouen Normandie, Rouen, France
The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 233-260.

In this paper, we propose to revisit a reciprocity gap method for solving point inverse source problem in an advection diffusion equation. The motivation of this problem is in ecology for pollutant source identification in a river. We propose the construction of original (numerically computed) adjoint functions that allows to consider more realistic geometries and river flows. The method is combined with a state estimator which allows to accelerate the identification process. The proposed method is validated on several examples.

Published online:
DOI: 10.5802/smai-jcm.124
Classification: 35K10, 35R30, 65M32
Keywords: Inverse source problem, advection diffusion equation, reciprocity gap method.

Antoine Tonnoir 1

1 LMI INSA Rouen Normandie, Rouen, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Combining reciprocity gap method and state estimator for source identification in an advection diffusion equation},
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     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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     year = {2025},
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Antoine Tonnoir. Combining reciprocity gap method and state estimator for source identification in an advection diffusion equation. The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 233-260. doi : 10.5802/smai-jcm.124. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.124/

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