We discuss, in this paper, a common flux-free method for the computation of strict error
bounds for linear and nonlinear finite-element computations. In the linear case, the error
bounds are on the energy norm of the error, while, in the nonlinear case, the concept of
error in constitutive relation is used. In both cases, the error bounds are strict in the
sense that they refer to the exact solution of the continuous equations, rather than to
some FE computation over a refined mesh. For both linear and nonlinear solid mechanics,
this method is based on the computation of a statically admissible stress field, which is
performed as a series of local problems on patches of elements. There is no requirement to
solve a previous problem of flux equilibration globally, as happens with other
methods.