A posteriori error estimation based on the superconvergent Recovery by Compatibility in Patches

The present work deals with an a posteriori error estimator for linear finite element analysis, based on a stress recovery procedure called Recovery by Compatibility in Patches. The key idea of this procedure is to recover improved stresses by minimizing the complementary energy over patches of elements. Displacements computed by the finite element analysis are prescribed on the boundary of the patch. Here, a new form of this recovery procedure is presented. Adopting a different patch configuration, centred upon an element instead of a node, allows to drastically simplify the recovery process, thus improving efficiency and making the implementation in finite element codes much easier. The robustness tests demonstrate that the error estimator associated to the new form of the recovery procedure retains the very good properties of the original one, such as superconvergence. The numerical results on two common benchmark problems confirm the effectiveness of the proposed error estimator, which appears to be competitive with those currently available.