Contraction property of adaptive hybridizable discontinuous galerkin methods

Bernardo Cockburn, Ricardo H. Nochetto, Wujun Zhang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We establish the contraction property between consecutive loops of adaptive hybridizable discontinuous Galerkin methods for the Poisson problem with homogeneous Dirichlet condition. The contractive quantity is the sum of the square of the L2-norm of the flux error, which is not even monotone, and a two-parameter scaled error estimator, which quantifies both the lack of H(div, Ω)-conformity and the deviation from a gradient of the approximate flux. A distinctive and novel feature of this analysis, which enables comparison between two nested meshes, is the lifting of trace residuals from inter-element boundaries to element interiors.

Original languageEnglish (US)
Pages (from-to)1113-1141
Number of pages29
JournalMathematics of Computation
Issue number299
StatePublished - Jan 1 2016

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