On the convergence rate of a difference solution of the Poisson equation with fully nonlocal constraints - Berikelashvilia, Givi; Khomeriki, Nodar (Nonlinear Analysis: Modelling and Control, 2014)
We consider the Poisson equation in a rectangular domain. Instead of the classical specification of boundary data, we impose an integral constraints on the inner stripe adjacent to boundary having the width ξ. The corresponding finite-difference scheme is constructed on a mesh, which selection does not depend on the value ξ. It is proved the unique solvability of the scheme. An a priori estimate of the discretization error is obtained with the help of energy inequality method. It is proved that the scheme is convergent with the convergence rate of order s-1, when the exact solution belongs to the fractional Sobolev space of order s (1<s ≤3).