"Richardson extrapolation for a convection-diffusion problem
using a Shishkin mesh"
by 
Maria Caridad Natividad\thanks{University of the Philippines,
Diliman, Quezon City, Philippines 1101; Email:
joanne@math.upd.edu.ph.  The work of M.C. Natividad was supported
by the Center of Excellence grant awarded to the Department of
Mathematics by the Philippine Commission on Higher Education }
and Martin Stynes\thanks{National University of Ireland, Cork, Ireland; Email: m.stynes@ucc.ie}}

Abstract:
We consider a convection-diffusion two-point boundary value
problem on a piecewise-uniform Shishkin mesh, and show that when
simple upwinding is used, a version of Richardson extrapolation
improves the accuracy of the computed solution (measured in the
discrete $L^\infty$ norm) from $O(N^{-1} \ln N)$ to $O(N^{-2}
\ln^{2}N)$, where $N+1$ mesh points are used. Numerical tests are
provided to support these theoretical results.