Modeling and simulation are central to a mechanical engineer's activity. Increasingly complex models are being used routinely on a daily basis. This revolution is the result of the extraordinary progress in computer technology in terms of both hardware and software.

This work deals with the control of the hypotheses leading from a mechanical model, usually coming from continuum mechanics, to a numerical model, i.e. the mastery of the mechanical computation process itself.  Particular attention is given to structural analysis which, in this context, is the most advanced domain.

A significant part of this work is dedicated to the application of error estimators to the control of the various parameters involved in a calculation, beginning with the parameters related to the mesh.

The notion of quality of a finite element solution.- The constitutive relation error method for linear problems.- Other methods for linear problems.- Principles of the comparison of the various estimators in the linear case.- Mesh adaptation for linear problems.- The constitutive relation error method for nonlinear evolution problems.- The constitutive relation error method in dynamics.- Techniques for constructing admissible fields.- Estimation of local errors.