In the numerical technique considered in this paper, time-stepping is performed on a set of semi-coarsened space grids. At given time levels the solutions on the different space grids are combined to obtain the asymptotic convergence 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-Crowley test) is used to assess the practical merits of the technique. The combination technique is shown to be more efficient than the single-grid approach, yet for the Molenkamp-Crowley test, standard Richardson extrapolation is still more efficient than the combination technique. However, parallelization is expected to significantly improve the combination technique's performance.

Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) (msc 41A58), Interpolation (msc 65D05), None of the above, but in MSC2010 section 65Gxx (msc 65G99), Multigrid methods; domain decomposition (msc 65M55)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Lastdrager, B, Koren, B, & Verwer, J.G. (1999). The sparse-grid combination technique applied to time-dependent advection problems. Modelling, Analysis and Simulation [MAS]. CWI.