Abstract. 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).
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