ERROR BOUNDS IN DUAL & COMPLEMENTARY EDDY‐CURRENT SYSTEMS

The formulation of electromagnetic field problems using dual and complementary energy methods is now well established, and the advantages of the error bounds to system energy for static systems that it provides are widely realized. When considering eddy‐current problems the picture is less clear, even for the restricted case of time harmonic fields. Several interesting papers have been published that address the particular question of whether or not error bounds can exist for such dissipative systems, but as yet no consensus view has emerged. This contribution is an attempt to help clarify the position. It will be shown that through the use of complementary variational principles it is possible to establish pairs of functionals that do indeed rigourously provide error bounds. Ilustrative examples show that it is usually possible to provide error bounds to eddy‐current system parameters so long as due care is taken to pre‐determine whether or not a particular problem may be regarded as either current driven, or voltage driven, from the circuit point of view.