Upper and Lower Bounding - An Equivalent Circuit Viewpoint

There has been considerable interest in complementary, bounding solutions to electromagnetic field problems over the last 10 years as a basis for an adapative solution, [1-3]. It is generally accepted that, for static, linear problems, the energy values obtained from a vector solution and those obtained from a scalar solution to the same problem approach the true solution from opposite sides, this providing a bounding nature. With one or two exceptions, little attention has been paid to the bounding in terms of eddy current systems, [4]. In fact, it is frequently considered that upper and lower bounding does not necessarily apply to such systems. It is the intention of this paper to discuss the behaviour of finite element solutions to electric, magnetic and eddy current field problems as the mesh is refined, from an equivalent circuit viewpoint.

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Upper and Lower Bounding - An Equivalent Circuit Viewpoint