V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes

In this paper we analyze the convergence properties of V -cycle multigrid algorithms for thenumerical solution of the linear system of equations stemming from discontinuous Galerkindiscretization of second-order elliptic partial differential equations on polytopic 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 algorithms with possible edge/facecoarsening. We prove that the method converges uniformly with respect to the granularity ofthe grid and the polynomial approximation degree p, provided that the minimum number ofsmoothing steps, which depends on p, is chosen sufficiently large.