An Equilibration Based A Posteriori Error Estimate for the Biharmonic Equation and Two Finite Element Methods
Numerical Analysis
2017-05-23 v1
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.
Keywords
Cite
@article{arxiv.1705.07607,
title = {An Equilibration Based A Posteriori Error Estimate for the Biharmonic Equation and Two Finite Element Methods},
author = {Dietrich Braess and Astrid S. Pechstein and J. Schöberl},
journal= {arXiv preprint arXiv:1705.07607},
year = {2017}
}