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

2017/05/22 by Dietrich Braess, Braess, Dietrich, Astrid Pechstein +3
Engineering · Mathematics · Physics and Astronomy · #65N15 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1705.07607

openalex publication_date 2017/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates

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