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arXiv · 1705.07607

An Equilibration Based A Posteriori Error Estimate for the Biharmonic Equation and Two Finite Element Methods

Dietrich Braess·Astrid S. Pechstein·J. Schöberl
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Abstract

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.

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Dietrich Braess, Astrid S. Pechstein, J. Schöberl. 2017-05-22. An Equilibration Based A Posteriori Error Estimate for the Biharmonic Equation and Two Finite Element Methods. https://arxiv.org/abs/1705.07607

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