By applying the mesh method error estimates of the approximate solution of the Laplace equation usually involves maximums of modules of derivatives of the desired solution. This naturally makes it difficult to use the estimates, in practice. Error estimates of some methods expressed by basic problem data are known in the references.

In this paper, first for a nonlocal mixed problem, the error of the Fourier discrete method is estimated effectively, i.e., the error is estimated with the help of the known data.

nonlocal mixed problem, difference scheme, approximate solution.