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Reconstruction of the right-hand side of the elliptical equation from observation data obtained at the boundary. (English) Zbl 1199.65373
Author’s abstract: We consider the classical inverse problem in potential theory in which it is required to determine the unknown right-hand side of the elliptic equation in the case in which additional data are set on the boundary of the calculation domain. To simplify the consideration, we restrict ourselves to the two-dimensional Poisson equation.

65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35R30 Inverse problems for PDEs