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A nite element method with optimal convergence on non-smooth three dimensional domains requires anisotropic mesh re nement towards the edges. Multigrid methods for anisotropic tensor product meshes are available and are based either on line (or plane) smoothers or on semi-coarsening strategies. In this paper we suggest and analyze a new multigrid scheme combining semi-coarsening and line smoothers to obtain a solver of optimal algorithmic complexity for anisotropic meshes along edges.doi:10.1137/s0036142900375414 fatcat:dbuvipz6wradjlrazsdslof2bi