Sponsor
Partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute
Published In
IMA Journal of Numerical Analysis
Document Type
Post-Print
Publication Date
10-2013
Subjects
Multigrid methods (Numerical analysis), Galerkin methods, Discontinuous functions
Abstract
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.
Rights
© 2013 by Cambridge University Press.
Locate the Document
DOI
10.1093/imanum/drt024
Persistent Identifier
http://archives.pdx.edu/ds/psu/10594
Citation Details
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.
Description
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.