Abstract To control the numerical quality of non-linear simulations allows to automate the choice of discretisation. Within the framework of time dependent problems, this quality depends on the error made in the calculation of the deformation history. Generally, a kind of expert analysis precedes the satisfying computation. In practice, this analysis could be an optimisation of numerical approximations. We propose a strategy herein, which naturally includes this expert analysis stage. The desired solution is built iteratively, improving all of the history at each iteration, thanks to the LATIN method. A global error estimator is provided by the dissipation error. To pilot the adaptive computation, we propose a partition of this estimator into indicators associated with each kind of error contribution.