Stability analysis of bitsadze-samarskii type overdetermined elliptic problem with dirichlet conditions

In this thesis, the stability estimates for the solution of the Dirichlet conditional Bitsadze-Samarskii type overdetermined problem for elliptic partial differential equations in the Hilbert space have been investigated. Stability and coercive stability estimates are obtained for the solution of the overdetermined problem. The first and second orders of the accuracy difference schemes are established for the approximate solutions of this overdetermined elliptic problem. Furthermore, after abstract solutions had been obtained, the first and second orders of the accuracy difference schemes of the Dirichlet conditional Bitsadze-Samarskii type overdetermined Dirichlet and Neumann boundary value problems are also established and stability analysis of the difference schemes are made. Finally, theoretical statements investigated for the difference schemes are confirmed by the results of the numerical examples.