A two-energies principle for the biharmonic equation and an a posteriori error estimator for an interior penalty discontinuous Galerkin approximation

We consider an a posteriori error estimator for the Interior Penalty Discontinuous Galerkin (IPDG) approximation of the biharmonic equation based on the Hellan-Herrmann-Johnson (HHJ) mixed formulation. The error estimator is derived from a two-energies principle for the HHJ formulation and amounts t...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2018-11, Vol.52 (6), p.2479-2504
Main Authors: Braess, Dietrich, Hoppe, R.H.W., Linsenmann, Christopher
Format: Article
Language:English
Subjects:
35J35
65N30
65N50
a posteriori error estimator
Approximation
Biharmonic equation
Biharmonic equations
equilibration
Errors
Galerkin method
interior penalty discontinuous Galerkin method
Interpolation
Mathematical analysis
Nonlinear programming
Tensors
two-energies principle
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Summary:We consider an a posteriori error estimator for the Interior Penalty Discontinuous Galerkin (IPDG) approximation of the biharmonic equation based on the Hellan-Herrmann-Johnson (HHJ) mixed formulation. The error estimator is derived from a two-energies principle for the HHJ formulation and amounts to the construction of an equilibrated moment tensor which is done by local interpolation. The reliability estimate is a direct consequence of the two-energies principle and does not involve generic constants. The efficiency of the estimator follows by showing that it can be bounded from above by a residual-type estimator known to be efficient. A documentation of numerical results illustrates the performance of the estimator.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2016074