A projection-based error analysis of HDG methods

Bernardo Cockburn, Jayadeep Gopalakrishnan, Francisco Javier Sayas

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152 Scopus citations

Abstract

We introduce a new technique for the error analysis of hybridizable discontinuous Galerkin (HDG) methods. The technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods. This renders the analysis of the projections of the discretization errors simple and concise. By showing that these projections of the errors are bounded in terms of the distance between the solution and its projection, our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection. We illustrate the technique on a specific HDG method applied to a model second-order elliptic problem.

Original languageEnglish (US)
Pages (from-to)1351-1367
Number of pages17
JournalMathematics of Computation
Volume79
Issue number271
DOIs
StatePublished - Jul 2010

Bibliographical note

Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

Keywords

  • Discontinuous Galerkin methods
  • Hybridization
  • Postprocessing
  • Superconvergence

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