High order of accuracy difference schemes for the inverse elliptic problem with Dirichlet condition
Department of Mathematical Engineering, Gumushane University, Gumushane, 29100, Turkey
TAU, 2009 Street, 143, Ashgabat, 744000, Turkmenistan
Boundary Value Problems 2014, 2014:5 doi:10.1186/1687-2770-2014-5Published: 7 January 2014
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.