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Combining reciprocity gap method and state estimator for source identification in an advection diffusion equation
Antoine Tonnoir1
1LMI 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 
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
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