In the numerical technique considered in this paper, time-stepping is perfo
rmed on a set of semi-coarsened space grids. At given time levels the solut
ions on the different space grids are combined to obtain the asymptotic con
vergence of a single, fine uniform grid. We present error estimates for the
two-dimensional, spatially constant-coefficient model problem and discuss
numerical examples. A spatially variable-coefficient problem (Molenkamp-Cro
wley test) is used to assess the practical merits of the technique. The com
bination technique is shown to be more efficient than the single-grid appro
ach, yet for the Molenkamp-Crowley test, standard Richardson extrapolation
is still more efficient than the combination technique. However, paralleliz
ation is expected to significantly improve the combination technique's perf
ormance. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights rese
rved.