Algebraic Analysis of Two-Level Multigrid Methods for Edge Elements

We present an algebraic analysis of two-level multigrid methods for the solution of linear systems arising from the discretization of the curl-curl boundary value problem with edge elements. The analysis is restricted to the singular compatible linear systems as obtained by setting to zero the contribution of the lowest order (mass) term in the associated partial differential equation. We use the analysis to show that for some discrete curl-curl problems, the convergence rate of some Reitzinger-Schoberl two-level multigrid variants is bounded independently of the mesh size and the problem peculiarities. This covers some discretizations on Cartesian grids, including problems with isotropic coefficients, anisotropic coefficients and/or stretched grids, and jumps in the coefficients, but also the discretizations on uniform unstructured simplex grids.