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In the context of global/goal-oriented error estimation applied tocomputational mechanics, the need to obtain reliable and guaranteed bounds onthe discretization error has motivated the use of residual error estimators.These estimators require the construction of admissible stress fields verifyingthe equilibrium exactly. This article focuses on a recent method, based on aflux-equilibration procedure and called the element equilibration + star-patchtechnique (EESPT), that provides for such stress fields. The standard versionrelies on a strong prolongation condition in order to calculate equilibratedtractions along finite element boundaries. Here, we propose an enhancedversion, which is based on a weak prolongation condition resulting in a localminimization of the complementary energy and leads to optimal tractions inselected regions. Geometric and error estimate criteria are introduced toselect the relevant zones for optimizing the tractions. We demonstrate how thisoptimization procedure is important and relevant to produce sharper estimatorsat affordable computational cost, especially when the error estimate criterionis used. Two- and three-dimensional numerical experiments demonstrate theefficiency of the improved technique.

An enhanced method with local energy minimization for the robust a posteriori construction of equilibrated stress fields in finite element analyses