A two-energies principle for the biharmonic equation and an a posteriori error estimator for an interior penalty discontinuous Galerkin approximation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2479-2504.

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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016074
Classification : 35J35, 65N30, 65N50
Mots-clés : Biharmonic equation, two-energies principle, interior penalty discontinuous Galerkin method, a posteriori error estimator, equilibration
Braess, Dietrich 1 ; Hoppe, R.H.W. 1 ; Linsenmann, Christopher 1

1 
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Braess, Dietrich; Hoppe, R.H.W.; Linsenmann, Christopher. A two-energies principle for the biharmonic equation and an a posteriori error estimator for an interior penalty discontinuous Galerkin approximation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2479-2504. doi : 10.1051/m2an/2016074. http://www.numdam.org/articles/10.1051/m2an/2016074/

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