Partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute
IMA Journal of Numerical Analysis
Multigrid methods (Numerical analysis), Galerkin methods, Discontinuous functions
We analyze the convergence of a multigrid algorithm for the Hybridizable Discontinuous Galerkin (HDG) method for diffusion problems. We prove that a non-nested multigrid V-cycle, with a single smoothing step per level, converges at a mesh independent rate. Along the way, we study conditioning of the HDG method, prove new error estimates for it, and identify an abstract class of problems for which a nonnested two-level multigrid cycle with one smoothing step converges even when the prolongation norm is greater than one. Numerical experiments verifying our theoretical results are presented.
Cockburn, Bernardo; Bubois, O.; and Gopalakrishnan, Jay, "Multigrid for an HDG Method" (2013). Mathematics and Statistics Faculty Publications and Presentations. 34.