2017/05/22 by Dietrich Braess, Braess, Dietrich, Astrid Pechstein +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #65N15 #65N30 #A priori and a posteriori #Advanced Numerical Methods in Computational Mathematics #Algorithm #Applied mathematics #Biharmonic equation #Boundary value problem #Classical mechanics #Computation #Computer science #Estimator #FOS: Mathematics #Finite element method #Galerkin method #Geometry #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Moment (physics) #Numerical Analysis (math.NA) #Numerical methods for differential equations #Physics #Space (punctuation) #Tensor (intrinsic definition)
paper · pdf · doi:10.48550/arxiv.1705.07607
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2017/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.