UPPER AND LOWER BOUNDS FOR LOCAL ELECTROMAGNETIC QUANTITIES

Most engineering problems are solved by means of numerical methods tha t are able to provide only approximate solutions, for which it would b e extremely useful to have efficient error estimators. Upper and lower bounds for quantities of integral character, like the stored magnetic energy or the ohmic power dissipated in the domain of interest, had b een clearly established along with the procedures to obtain them numer ically. However, upper and lower bounds for local quantities would be of paramount interest in several fields of applications like Non-Destr uctive Testing or Nuclear Magnetic Resonance. We present here a proced ure for the determination of upper and lower bounds of local field qua ntities, namely the average value of a held component in an arbitraril y small region. It is based on the introduction of an auxiliary field, and is the natural extension of the method establishing the bounds of global quantities. Our technique can be used for any linear system in stationary conditions for which a virtual work principle can be appli ed. Its efficiency is demonstrated with the analysis of some stationar y 2D and 3D electromagnetic problems. (C) 1998 John Wiley & Sons, Ltd.