Distributive smoothers in multigrid for problems with dominating grad-div operators

In this paper, we present efficient multigrid methods for systems of partial differential equations that are governed by a dominating grad-div operator. In particular, we show that distributive smoothing methods give multigrid convergence factors that are independent of problem parameters and of the mesh sizes in space and time. The applications range from model problems to secondary consolidation Biot's model. We focus oil the smoothing issue and mainly solve academic problems on Cartesian-staggered grids. Copyright (C) 2008 John Wiley & Sons, Ltd.