Subdomain - based flux - free a posteriori error estimators ⋆ Núria PARÉS , Pedro DÍEZ and Antonio HUERTA ∗

A new residual-type flux-free error estimator is presented. It computes upper and lower bounds of the error in energy norm with the ultimate goal of obtaining bounds for outputs of interest. The proposed approach precludes the main drawbacks of standard residual type estimators circumventing the need of flux-equilibration and resulting in a simple implementation that uses standard resources available in finite element codes. This is especially interesting for existing codes and 3D applications where the implementation of this technique is as simple as in 2D. Recall that on the contrary, the complexity of the flux-equilibration techniques increases drastically in the 3D case. Bounds for the energy norm of the error are used to produce upper and lower bounds of linear functional outputs, representing quantities of engineering interest. This new flux-free error estimator improves the effectivity of previous approaches (better accuracy in every test) and it can be used in the mechanical case for linear elements. The proposed approach demonstrates its efficiency in numerical tests producing sharp bounds of the reference error both for the energy and the quantities of interest.