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.
Lastdrager, B., Koren, B., & Verwer, J. G. (2001). The sparse-grid combination technique applied to time-dependent advection problems. Applied Numerical Mathematics, 38(4), 377-401. https://doi.org/10.1016/S0168-9274(01)00030-7