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Finite elements in computational electromagnetism

Published online by Cambridge University Press:  15 July 2003

R. Hiptmair
Affiliation:
Sonderforschungsbereich 382, Universität Tübingen, D-72076 Tübingen, Germany. E-mail: [email protected]

Abstract

This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete differential forms represent a genuine generalization of conventional Lagrangian finite elements, the analysis is based upon a judicious adaptation of established techniques in the theory of finite elements. Risks and difficulties haunting finite element schemes that do not fit the framework of discrete differential forms are highlighted.

Type
Research Article
Copyright
© Cambridge University Press 2002

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