The sparse-grid combination technique applied to time-dependent advection problems

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.