Volume 52, Number 6, November-December 2018
|Page(s)||2479 - 2504|
|Published online||14 February 2019|
A two-energies principle for the biharmonic equation and an a posteriori error estimator for an interior penalty discontinuous Galerkin approximation⋆
Faculty of Mathematics, Ruhr-University, 44780 Bochum, Germany
2 Dept. of Math. Univ. of Houston Houston, TX 77204-3008, U.S.A
3 Inst. of Math., Univ. of Augsburg, 86159 Augsburg, Germany
Accepted: 23 November 2016
We consider an a posteriori error 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.
Mathematics Subject Classification: 35J35 / 65N30 / 65N50
Key words: Biharmonic equation / two-energies principle / interior penalty discontinuous Galerkin method / a posteriori error estimator / equilibration
© EDP Sciences, SMAI 2019
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