HEJ, HU ISSN 1418-7108 Manuscript no.: ANM-981030-A

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A Mixed Variational Formulation for 3D Linear and Nonlinear Magnetostatics in the Space ${H_0}({\rm rot}) \cap {H}({\rm div})$

B. Heise$^\ast$ and M. Kuhn$^\ast$ and U. Langer¹

Abstract:

In the present paper, mixed variational formulations that consider the problems of gauging and interface conditions in a quite natural way are analyzed for magnetostatics. Standard results with respect to the Ladyzenskaya-Babuška-Brezzi (LBB) condition can be carried over from Stokes problems to electro-magnetic fields. Nonlinear problems are analyzed and the existence of a unique solution is shown under appropriate assumptions.

Keywords: Nonlinear Magnetostatic Problems, Mixed Problems

HEJ, HU ISSN 1418-7108 Manuscript no.: ANM-981030-A