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.
|Title of host publication||Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999)|
|Editors||E. Dick, K. Riemslagh, J. Vierendeels|
|Place of Publication||Berlin|
|Publication status||Published - 2000|
|Name||Lecture Notes in Computational Science and Engineering|