We analyse the convergence of a multigrid algorithm for the hybridizable discontinuous Galerkin (HDG) method for diffusion problems. We prove that a nonnested 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 non-nested two-level multigrid cycle with one smoothing step converges even when the prolongation norm is greater than 1. Numerical experiments verifying our theoretical results are presented.
Bibliographical noteFunding Information:
This research was partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute (to B.C.) and supported in part by the National Science Foundation under Grant DMS-1211635 (to J.G.).
© 2013 The authors. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
- discontinuous Galerkin methods
- hybrid methods
- multigrid methods