This paper deals with grid approximations to Prandtl's boundary value
problem for boundary layer equations on a flat plate in a region
including the boundary layer, but outside a neighbourhood of its
leading edge. The perturbation parameter
e=1/*Re* takes any values
from the half-interval (0,1]; here *Re* is the Reynolds number.
To demonstrate our numerical techniques we consider the case of
the self-similar solution. By using piecewise uniform meshes,
which are refined in a neighbourhood of the parabolic boundary layer,
we construct a finite difference scheme that converges
e-uniformly. We present the technique
of experimental substantiation of e-uniform
convergence for both the numerical solution and its normalized (scaled) difference
derivatives, outside a neighbourhood of the leading edge of the plate.
By numerical experiments we demonstrate the efficiency of numerical
techniques based on the fitted mesh method.
We discuss also the applicability of fitted operator methods for
the numerical approximation of the Prandtl problem.
It is shown that the use of meshes refined in
the parabolic boundary layer region is necessary for achieving
e-uniform convergence.