A Fourth Order Approximation of the Neumann Type Overdetermined Elliptic Problem

Abstract

In this paper, we consider inverse elliptic problem with Neumann type overdetermination and construct a fourth order of accuracy difference scheme for its solution. Stability, almost coercive stability and coercive stability estimates for the solution of difference problem are proved. Later, we construct a fourth order difference scheme for inverse problem for multidimensional elliptic equation with Neumann type overdetermination and Dirichlet boundary condition. Finally, we illustrate numerical example with the descriptions of numeric realization in
a two-dimensional case.