O. J. B. Almeida Pereira and J. P. Moitinho de Almeida
From the dual analysis of an equilibrium finite element model and a conventional displacement finite element model, a local error indicator and an upper bound of the global error can be obtained. As both an equilibrated stress field and a compatible displacement field are available for output and the element error indicator is computed through a simple integration, no smoothing or expensive a posteriori error analysis are needed. The analysis of the two models can be done in parallel, using two processors, in approximately the same time as a conventional analysis. The equilibrium finite element formulation, the error indicator and the error estimator are described. An example in three-dimensional elastostatics is presented.