A posteriori error estimates for HDG methods

Bernardo Cockburn, Wujun Zhang

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We present the first a posteriori error analysis of the so-called hybridizable discontinuous Galerkin (HDG) methods for second-order elliptic problems. We show that the error in the flux can be controlled by only two terms. The first term captures the so-called data oscillation. The second solely depends on the difference between the trace of the scalar approximation and the corresponding numerical trace. Numerical experiments verifying the reliability and efficiency of the estimate in two-space dimensions are presented.

Original languageEnglish (US)
Pages (from-to)582-607
Number of pages26
JournalJournal of Scientific Computing
Volume51
Issue number3
DOIs
StatePublished - Jan 1 2012

Keywords

  • A posteriori error estimate
  • Discontinuous Galerkin method
  • Postprocessing solution

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