Abstract
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.
Original language | English (US) |
---|---|
Pages (from-to) | 1386-1425 |
Number of pages | 40 |
Journal | IMA Journal of Numerical Analysis |
Volume | 34 |
Issue number | 4 |
DOIs | |
State | Published - Apr 16 2014 |
Bibliographical note
Publisher Copyright:© 2013 The authors. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Keywords
- discontinuous Galerkin methods
- hybrid methods
- multigrid methods