TY - JOUR
T1 - Contraction property of adaptive hybridizable discontinuous galerkin methods
AU - Cockburn, Bernardo
AU - Nochetto, Ricardo H.
AU - Zhang, Wujun
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
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U2 - 10.1090/mcom/3014
DO - 10.1090/mcom/3014
M3 - Article
AN - SCOPUS:84959455409
VL - 85
SP - 1113
EP - 1141
JO - Mathematics of Computation
JF - Mathematics of Computation
SN - 0025-5718
IS - 299
ER -