Abstract :
A method to construct grid approximations for singularly perturbed boundary
value problems for elliptic and parabolic equations, whose solutions contain a
parabolic boundary layer, is considered. The grid approximations are based on the
fitted operator method. Finite difference schemes, finite element, or finite volume
techniques are included in the term grid approximation methods. It is shown that
there exists no grid approximation method on uniform grids from the class of fitted
operator methods, whose solutions converge, in the discrete maximum norm,
uniformly with respect to the perturbation parameter to the solution of the
boundary value problem.
