V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes - Antonietti, P. F.; Pennesi, G. (Journal of scientific computing, 2019)
In this paper we analyze the convergence properties of V -cycle multigrid algorithms for the numerical solution of the linear system of equations stemming from discontinuous Galerkin discretization 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/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 minimum number of smoothing steps, which depends on p , is chosen sufficiently large.