# 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

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0006.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**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.