Multigrid for an HDG method

B. Cockburn, O. Dubois, J. Gopalakrishnan, S. Tan

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

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 languageEnglish (US)
Pages (from-to)1386-1425
Number of pages40
JournalIMA Journal of Numerical Analysis
Volume34
Issue number4
DOIs
StatePublished - Apr 16 2014

Bibliographical note

Funding 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.).

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

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