Inverse Neumann problem for an equation of elliptic type

Inverse problem for an elliptic differential equation with Neumann conditions is considered. Stability and coercive stability estimates for the solution of inverse problem with the overdetermination are obtained. The first and second order of accuracy difference schemes are presented. Stability and coercive stability inequalities for these difference schemes are given. In application, inverse problem for the multidimensional elliptic equation is studied. The first and second order of accuracy difference schemes for the multidimensional inverse problem are presented. Well-posedness of both difference problems are established. The results are supported by a numerical example for the two-dimensional elliptic equation.