Slimani, S.; Medarhri, I.; Najib, K.; Zine, A. Identification of the source function for a seawater intrusion problem in unconfined aquifer. (English) Zbl 1453.65292 Numer. Algorithms 84, No. 4, 1565-1587 (2020). Summary: In this work, we study the inverse source problem of a seawater intrusion problem in an unconfined aquifer with sharp-diffuse interfaces. The model associated with the direct problem is nonlinear. We aim to reconstruct the source term following the technique used in [M. Kulbay et al., Inverse Probl. Sci. Eng. 25, No. 2, 279–308 (2017; Zbl 1362.80005)]. As this technique is based on variable separation, a fixed-point strategy is adopted to linearize the problem. Numerical convergence is proven using some examples. Cited in 1 Document MSC: 65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs 65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 76S05 Flows in porous media; filtration; seepage 35R35 Free boundary problems for PDEs 76M10 Finite element methods applied to problems in fluid mechanics 86A05 Hydrology, hydrography, oceanography 86A22 Inverse problems in geophysics 65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization 65F22 Ill-posedness and regularization problems in numerical linear algebra Keywords:inverse source problem; seawater intrusion problem; fixed point theorem; numerical analysis Citations:Zbl 1362.80005 Software:corner.m PDFBibTeX XMLCite \textit{S. 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