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Data completion problem for the advection‐diffusion equation with aquifer point sources

We consider the inverse problem of recovering the missing flux and concentration on some part of a boundary of an aquifer using overspecified measurements available on some accessible part. The aquifer is under the action of point‐forces located inside the domain and governed by the advection‐diffusion equation. The method used is based on a fictitious domain decomposition. Numerical tests are done attesting the performance of the identification process.