On the Convergence Rate of the Finite-Difference Solution of a Nonlocal Boundary Value Problem for a Second-Order Elliptic Equation

Abstract

2 )t o the exact solution in the class C 4 was considered in [5] in the case of the Poisson equation. In the present paper, we consider a nonlocal Bitsadze{Samarskii boundary value problem for a second-order elliptic equation with constant coecients in the unit square . The approximation suggested in [5] is used for the nonlocal condition. The corresponding dierence scheme is studied in weighted Sobolev spaces. Under the assumption that the solution of the original problem belongs to a Sobolev{Slobodetskii space, we estimate the convergence rate as ky ukWk 2 (!;r) ch s k kukWs 2 () ;s 2 (k;k +2 ] ;k =1 ; 2;