Strict error bounds in linear solid mechanics using a subdomain-based flux-free approach

Abstract

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.