Practical numerical solvers for boundary problems require assessing the resulting accuracy. Error was used to be measured using the energy norm but, currently, the error is preferred to be evaluated using quantities of interest defined by the end user. The error representation for these magnitudes requires solving both the original problem (primal) and an adjoint problem (dual) associated with the quantity of interest, that have to be combined. The representation of the error, i.e. the way of combining them, is not unique. Here, three error representations are analyzed combined with different recovery procedures. The ideas introduced by Zienkiewicz & Zhu (1987 & 1992) for stress recovery and by Wiberg (1992) for displacements are used. The numerical tests analyze the performance of the proposed methodologies both in thermal and mechanical problems. Implementation aspects are also discussed, especially in the framework of adaptive remeshing processes.

O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Int. J. Numer. Meth. Engr. 33, pp. 1331--1365, (1992).

N.E. Wiberg, L.F. Zeng and X.D. Li, Error estimation and adaptivity in elastodynamics, Comput. Methods Appl. Mech
Engrg., Vol. 101, pp. 369--395, (1992).

N.E. Wiberg and X.D. Li, Superconvergent patch recovery of finite-element and a posteriori L2 norm error estimate, Comm.
in Numer. Meth. Engr., Vol. 10, pp. 313--320, (1994).