This paper deals with adaptive meshing in the case of time dependent problems within a 3D non linear multi-static approximation. In order to evaluate the numerical errors, the notion of ligurian is introduced. This estimator requires a couple of admissible fields. A method for the determination of this last couple is exposed. At least, on a three-phased transformer, we highlight the difficulties of the calculation of a well adapted error distribution for adaptive meshing. Three methods are exposed and compared.