[Zurück]

D. Braess, A. Pechstein, J. Schöberl:
"An Equilibration Based A Posteriori Error Estimate for the Biharmonic Equation and Two Finite Element Methods";
arXiv.org e-Print archive, 1705 (2017), 7607; 20 S.

We develop an a posteriori error estimator for the Interior Penalty Discontinuous Galerkin approximation of the biharmonic equation with continuous finite elements. The error bound is based on the two-energies principle and requires the computation of an equilibrated moment tensor. The natural space for the moment tensor consists of symmetric tensor fields with continuous normal-normal components. It is known from the Hellan-Herrmann-Johnson (HHJ) mixed formulation. We propose a construction that is totally local. The procedure can also be applied to the original HHJ formulation, which directly provides an equilibrated moment tensor.

http://publik.tuwien.ac.at/files/publik_263016.pdf