Robust multigrid methods for nonsmooth coefficient elliptic linear systems

We survey the literature on robust multigrid methods which have been developed in recent years for solving second-order elliptic PDEs with nonsmooth coefficients. We highlight the key ideas of designing robust multigrid methods which are able to recover the usual multigrid efficiency for nonsmooth coefficient PDEs on structured or unstructured grids. In particular, we shall describe various approaches for constructing the interpolation and the smoothing operators, and the coarse grid points selections.