Contraction property of adaptive hybridizable discontinuous Galerkin methods

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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.

Bernardo Cockburn, Ricardo H. Nochetto, Wujun Zhan

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