Some improvements to the flux-type a posteriori error estimators

This paper presents explicit equilibrated fluxes for the local pure-Neumann problems used by the a posteriori error estimator in Ainsworth and Oden [M. Ainsworth, J.T. Oden, A procedure for a posteriori error estimation for h–p finite element methods, Comput. Methods Appl. Mech. Engrg. 101 (1992) 73–96]. We modify the target function for minimization to obtain new equilibrated fluxes in a weighted form. We investigate the performance of the new equilibrated fluxes in two-dimensional spectral/hp element approximations of an elliptic equation using conforming triangle elements. The new fluxes appear more robust and lead to substantial computational savings compared to the original numerical procedure in Ainsworth and Oden [Ainsworth and Oden et al., 1992].