A finite difference method for the inverse elliptic problem with the Dirichlet condition

Abstract

Well-posedness of the inverse problem for the elliptic differential equation with Dirichlet condition is investigated. A finite difference method for the approximate solution of the inverse problem is applied. Stability and coercive stability estimates for the solution of the first and second order of accuracy difference schemes are obtained. In applications, the inverse problem for the multidimensional elliptic equation is studied. The theoretical statements are supported by the numerical example in a two dimensional case of elliptic equation.