A two-energies principle for the biharmonic equation and ana posteriorierror estimator for an interior penalty discontinuous Galerkin approximation
2018 ◽
Vol 52
(6)
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pp. 2479-2504
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Keyword(s):
We consider ana posteriorierror estimator for the Interior Penalty Discontinuous Galerkin (IPDG) approximation of the biharmonic equation based on the Hellan-Herrmann-Johnson (HHJ) mixed formulation. The error estimator is derived from a two-energies principle for the HHJ formulation and amounts to the construction of an equilibrated moment tensor which is done by local interpolation. The reliability estimate is a direct consequence of the two-energies principle and does not involve generic constants. The efficiency of the estimator follows by showing that it can be bounded from above by a residual-type estimator known to be efficient. A documentation of numerical results illustrates the performance of the estimator.
2021 ◽
Vol 36
(6)
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pp. 313-336
2019 ◽
Vol 40
(2)
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pp. 951-975
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Keyword(s):
2014 ◽
Vol 52
(4)
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pp. 2121-2136
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2014 ◽
Vol 14
(1)
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pp. 71-87
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2011 ◽
Vol 200
(21-22)
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pp. 1877-1891
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2013 ◽
Vol 14
(3)
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pp. 753-779
2006 ◽
Vol 30
(3)
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pp. 465-491
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