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This paper focuses on the construction of statically admissible stress fields(SA-fields) for a posteriori error estimation. In the context of verification,the recovery of such fields enables to provide strict upper bounds of theenergy norm of the discretization error between the known finite elementsolution and the unavailable exact solution. The reconstruction is a difficultand decisive step insofar as the effectiveness of the estimator stronglydepends on the quality of the SA-fields. This paper examines the strongprolongation hypothesis, which is the starting point of the ElementEquilibration Technique (EET). We manage to characterize the full space ofSA-fields satisfying the prolongation equation so that optimizing inside thisspace is possible. The computation exploits topological properties of the meshso that implementation is easy and costs remain controlled. In this paper, wedescribe the new technique in details and compare it to the classical EET andto the flux-free technique for different 2D mechanical problems. The method isexplained on first degree triangular elements, but we show how extensions todifferent elements and to 3D are straightforward.

Study of the strong prolongation equation for the construction of statically admissible stress fields: implementation and optimization