High Order Approximation of the Inverse Elliptic Problem with Dirichlet-Neumann Conditions

Abstract

Inverse problem for the multidimensional elliptic equation with Dirichlet-Neumann conditions is considered. High order of accuracy difference schemes for the solution of inverse problem are presented. Stability, almost coercive stability and coercive stability estimates of the third and fourth orders of accuracy difference schemes for this problem are obtained. Numerical results in a two dimensional case are given.