A technique for computing realistic values of the error parameters for the numerical solutions of singular perturbation problems

In this paper we describe an experimental technique to determine approximate values of the error parameters associated with a parameter-uniform numerical method for solving singularly perturbed convection-diffusion problems. We employ the technique to compute realistic values of these parameters for the numerical solutions generated by a monotone parameter-uniform numerical method applied to an elliptic boundary value problem with different types of boundary layers such as regular, parabolic and corner layers. Such error parameters allow us effectively to evaluate actual error bounds for the numerical solutions and to determine the parameter-uniformity of new numerical methods and, therefore, their applicability in practice.