Dual and complementary energy methods in electromagnetism

Abstract

The use of dual and complementary variational formulations of the electromagnetic field equations is reviewed and the usefulness of such techniques explored. Particular attention is devoted to the efficient implementation of these methods in conjunction with the finite element method, and wider areas of application discussed. The use of such techniques in the development of a general structure for the field equations is outlined, and examples chosen from electrostatics, magnetostatics and time varying problems show how error bounded solutions may be achieved.