2008 , Volume 13, № 3, p.45-53

For a function of two variables, corresponding to a solution of the elliptic problem with a boundary layer, the interpolation function is constructed. It is shown, that interpolation error is small for any relations between a small parameter and mesh steps. It is proved, that in case of the Shishkin mesh polinomial interpolation the method is uniformly accurate with regard to a small parameter. Formulas for calculation of derivatives, that use mesh values of the solution with a uniformly small error are proposed.