Method of interpolation for a function of two variables with a boundarylayer component
For a function of two variables, corresponding to a solution of the elliptic problemwith a boundary layer, the interpolation function is constructed. It is shown, thatinterpolation error is small for any relations between a small parameter and meshsteps. It is proved, that in case of the Shishkin mesh polinomial interpolation themethod is uniformly accurate with regard to a small parameter. Formulas for calculationof derivatives, that use mesh values of the solution with a uniformly small error areproposed.