This paper deals with adaptive meshing in the case of time dependent proble
ms 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 t
his last couple is exposed. At least, on a three-phased transformer, we hig
hlight the difficulties of the calculation of a well adapted error distribu
tion for adaptive meshing. Three methods are exposed and compared.