Hostname: page-component-84b7d79bbc-l82ql Total loading time: 0 Render date: 2024-07-26T19:20:29.398Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Arthurs, A. M.Proc. Roy. Soc. Ser. A 298 (1967), 97–101.Google Scholar
(2)Arthurs, A. M. and Robinson, P. D.Proc. Roy. Soc. Ser A 303 (1968), 497–509.Google Scholar
(3)Arthurs, A. M. and Robinson, P. D.Proc. Cambridge Philos Soc. 65 (1969), 535–541.CrossRefGoogle Scholar
(4)Courant, R. and Hilbert, D.Methods of mathematical physics, vol. 1 (Interscience, 1953).Google Scholar
(5)Schrader, D. M.J. Math. Phys. 8 (1967), 870–872.CrossRefGoogle Scholar
(6)Synge, J. L.The hypercircle in mathematical physics (Cambridge University Press, 1957).CrossRefGoogle Scholar