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.

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Modelling, Analysis and Simulation [MAS]
Scientific Computing

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