A third order of accuracy difference scheme for the Neumann type overdetermined elliptic problem

Abstract

In this paper, a third order of accuracy approximation of the solution of elliptic identification problem with Neumann type overdetermination is presented. We obtain stability estimates for the solutions of constructed difference scheme. Furthermore, a third order of accuracy difference scheme for Neumann type overdetermined multidimensional elliptic problem with Dirichlet boundary condition is constructed. Finally, a numerical example for two-dimensional problem is given.