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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.

modélisation mathématique et analyse numérique

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

A two-energies principle for the biharmonic equation and ana posteriorierror estimator for an interior penalty discontinuous Galerkin approximation