A posteriori error analysis for hybridizable discontinuous Galerkin methods for second order elliptic problems

Bernardo Cockburn, Wujun Zhang

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We present a unified a posteriori error analysis for hybridizable discontinuous Galerkin methods for second order elliptic partial differential equations. The main feature of this analysis is that it reduces the task of establishing the reliability and efficiency of the estimator to the verification of three simple conditions. This approach allows us not only to derive new estimates for hybridizable discontinuous Galerkin methods but also to recover well-known a posteriori error estimates for mixed methods and for the continuous Galerkin method.

Original languageEnglish (US)
Pages (from-to)676-693
Number of pages18
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number1
DOIs
StatePublished - Apr 17 2013

Keywords

  • A posteriori error analysis
  • Discontinuous Galerkin methods
  • Postprocessing

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