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

Boundary value problems

Charyyar Ashyralyyev¹ 

[1] Department of Mathematical Engineering, Gumushane University, Gumushane, Turkey

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

DOI  :  10.1186/1687-2770-2014-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY