Summary: We provide some extensions to the algebraic multigrid method based on element interpolation (AMGe), concerning the agglomeration process, the application to nonconforming elements, and the application to the mixed finite element discretization of the Oseen linearized Navier–Stokes equations. This last point, using AMGe for mixed finite elements, becomes straightforward because of the availability of coarse-level topologies. We show this exemplarily for the Crouzeix-Raviart element (including a stability result).
The numerical results show that it really pays off to take a closer look at the agglomeration strategy. A ‘wrong’ choice can lead to insufficient convergence or even divergence of the overall multigrid method.