Abstract.

We consider the inverse problem of determining, together with the solution, the location, and intensity of a point source in the advection-dispersion-reaction equation using two point measurements located on both sides relative to the source. The equation is supplemented by initial and boundary conditions of the Neumann or Dirichlet type. The theoretical review of this inverse problem is considered in many articles, both in one-dimensional and multidimensional cases. However, most of them are based on reducing the problem to an optimal control problem and minimizing the corresponding functional. As a rule, this requires large computational capabilities and does not always lead to the desired result. The paper provides a description of the numerical algorithm scheme. The numerical algorithm for determining the location of the source and solving the inverse problem is justified by using an explicit asymptotic formula. The intensity is determined by the Duhamel formula. The numerical implementation is based on the finite element method and the finite difference method for the corresponding system of ordinary differential equations. Numerical experiments for two groups of input data were performed. The results of numerical experiments to restore the location and intensity of the sources are presented. Numerical experiments demonstrate good convergence.

Keywords:

parabolic equation, inverse problem, finite element method, source function.

PP. 46-54.

DOI: 10.14357/20790279190406

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