Complementary and dual energy finite element principles in magnetostatics

A method of providing bounded solutions to a wide range of magnetostatic field problems is outlined. The method extends complementary and dual energy variational principles to encompass the T-Ω formulation of electromagnetic field problems and shows how this leads to efficient finite element implementation of the technique. Examples are given that show clearly the bounded nature of the procedure, and indicate how it may be used to reduce the computational requirements necessary for a specific accuracy of solution.