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Extremum principles for electrostatic and magnetostatic problems

Published online by Cambridge University Press:  24 October 2008

A. M. Arthurs  and
P. D. Robinson
A. M. Arthurs
Affiliation:
Department of Mathematics, University of York
P. D. Robinson
Affiliation:
Department of Mathematics, University of York
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Abstract

Complementary variational principles are derived for a class of electrostatic and magnetostatic problems using the pairs of adjoint operators (grad, – div) and (curl, curl). This theory unifies the principles of Dirichlet and Thomson in electrostatics and of Schrader in magnetostatics. The results are illustrated by deriving upper and lower bounds for the capacity of a surface, and it is shown how such bounds can be systematically improved by Ritz procedures.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 433 - 436
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

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