Combining reciprocity gap method and state estimator for source identification in an advection diffusion equation

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.