Poisson equation in polyhedral domain О C Rn […], n = 2,3 with boundary Г […], when Dirichlet conditions are given on all faces or on all but one where Neimann conditions are given, is considered. Traditional difference schemes with semi-constant steps along axes precisely approximate Dirichlet conditions hence it is expected that their accuracy order increases approaching to corresponding part of boundary ф […]. This paper is dedicated to quantitative investigation of this boundary effect. It is also shown that analogous boundary effect in the mesh knots takes place also for finite-element method (super convergence). The shorten version of this paper is published in [9].
