Guaranteed computable bounds for the exact error in the finite element solution - Part II: bounds for the energy norm of the error in two dimensions

This paper addresses the computation of guaranteed upper and lower bounds for the energy norm of the exact error in the nite element solution. These bounds are constructed in terms of the solutions of local residual problems with equilibrated residual loads and are rather sharp, even for coarse meshes. The sharpness of the bounds can be further improved by employing a few iterations of a relatively inexpensive iterative scheme. The main result is that the bounds are guaranteed for the energy norm of the exact error, unlike the bounds which have been proposed in [13,14] which are guaranteed only for the energy norm of the error with respect to an enriched (truth-mesh) nite element solution