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 f or the energy norm of the exact error in the finite element solution. These bounds are constructed in terms of the solutions of local residual problem s with equilibrated residual loads and are rather sharp, even for coarse me shes. The sharpness of the bounds can be further improved by employing a fe w iterations of a relatively inexpensive iterative scheme. The main result is that the bounds are guaranteed far the energy norm of the exact error, u nlike 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-me sh) finite element solution. Copyright (C) 2000 john Wiley & Sons, Ltd.