An experimental technique for computing parameter-uniform error estimates for numerical solutions of singular perturbation problems, with an application to Prandtl's problem at high Reynolds number

In this paper we describe an experimental technique for computing realistic values of the parameter-uniform order of convergence and error constant in the maximum norm associated with a parameter-uniform numerical method for solving singularly perturbed problems. We employ the technique to compute Reynolds-uniform error bounds in the maximum norm for the numerical solutions generated by a fitted-mesh upwind finite difference method applied to Prandtl's problem arising from laminar flow past a thin flat plate. Thus we illustrate the efficiency of the technique for finding realistic parameter-uniform error bounds in the maximum norm for the approximate solutions generated by numerical methods for which no theoretical error analysis is available.