In this paper, we derive, in the framework of the ux-free method, strict bounds for the energy norm of the error associated to a finite element computation. In that framework, and when using linear elements, the problems posed on the subdomains are solvable only when modified by the introduction of a projection operator in the residual.
We introduce a new such operator, and show that, in the context of a dual formulation,
it further allows to construct statically admissible fields over each subdomain. When
combined, these local stress fields provide the desired strict bound.