Computing realistic Reynolds-uniform error bounds for discrete derivatives of flow velocities in the boundary layer for Prandtl's problem

In this paper, we describe an experimental error analysis 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 then employ this technique to compute Reynolds-uniform error bounds in the maximum norm for appropriately scaled discrete derivatives of 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. Here the singular perturbation parameter is the reciprocal of the Reynolds number. This illustrates the efficiency of the technique for finding realistic parameter-uniform error bounds in the maximum norm for numerical approximations to scaled derivatives of solutions to problems in cases where no theoretical error analysis is available.