Open Access Research

High order of accuracy difference schemes for the inverse elliptic problem with Dirichlet condition

Charyyar Ashyralyyev

Author Affiliations

Department of Mathematical Engineering, Gumushane University, Gumushane, 29100, Turkey

TAU, 2009 Street, 143, Ashgabat, 744000, Turkmenistan

Boundary Value Problems 2014, 2014:5  doi:10.1186/1687-2770-2014-5

Published: 7 January 2014

Abstract

The overdetermination problem for elliptic differential equation with Dirichlet boundary condition is considered. The third and fourth orders of accuracy stable difference schemes for the solution of this inverse problem are presented. Stability, almost coercive stability, and coercive inequalities for the solutions of difference problems are established. As a result of the application of established abstract theorems, we get well-posedness of high order difference schemes of the inverse problem for a multidimensional elliptic equation. The theoretical statements are supported by a numerical example.

MSC: 35N25, 39A14, 39A30, 65J22.

Keywords:
difference scheme; inverse elliptic problem; high order accuracy; well-posedness; stability; almost coercive stability; coercive stability