Title: V-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes,
Abstract: In this paper we analyse the convergence properties of V-cycle multigrid
algorithms for the numerical solution of the linear system of equations arising
from discontinuous Galerkin discretization of second-order elliptic partial
differential equations on polytopal meshes. Here, the sequence of spaces that
stands at the basis of the multigrid scheme is possibly non nested and is
obtained based on employing agglomeration with possible edge/face coarsening.
We prove that the method converges uniformly with respect to the granularity of
the grid and the polynomial approximation degree p, provided that the number of
smoothing steps, which depends on p, is chosen sufficiently large.