  A generalized constitutive relation error is proposed in an analogous form to
Fenchel-Young inequality on the basis of the key idea of Legendre-Fenchel
duality theory. The generalized constitutive relation error is linked with the
global errors of some admissible solutions for the problem in question, and is
of wide applicability, especially in a posteriori error estimations of
numerical methods. A class of elliptic variational inequalities is examined
using the proposed approach and a strict upper bound of global energy errors of
admissible solutions is obtained.
