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Multigrid for an HDG Method
IMA Journal of Numerical Analysis
  • Bernardo Cockburn, University of Minnesota - Twin Cities
  • O. Bubois, Ecole Polytechnique de Montreal
  • Jay Gopalakrishnan, Portland State University
Document Type
Publication Date
  • 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.


© 2013 by Cambridge University Press.


NOTICE: this is the author’s version of a work that was accepted for publication in IMA Journal of Numerical Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in IMA Journal of Numerical Analysis, 34(4), 1386-1425.

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Citation Information
Published as: Cockburn, B., Dubois, O., Gopalakrishnan, J., & Tan, S. (2014). Multigrid for an HDG method. IMA Journal of Numerical Analysis, 34(4), 1386-1425.