Analysis of a kinematic dynamo model with FEM-BEM coupling

We consider a kinematic dynamo model in a bounded interior simply connected region Ω and in an insulating exterior region Ωc:=R3∖Ω¯. In the so‐called direct problem, the magnetic field B and the electric field E are unknown and are driven by a given incompressible flow field w. After eliminating E,...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2014-11, Vol.37 (16), p.2484-2501
Main Authors: Lemster, W., Lube, G., Of, G., Steinbach, O.
Format: Article
Language:English
Subjects:
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Exteriors
FEM-BEM coupling
Joining
Kinematics
Magnetic fields
magnetohydrodynamics
Mathematical analysis
Mathematical models
Rotating generators
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Summary:We consider a kinematic dynamo model in a bounded interior simply connected region Ω and in an insulating exterior region Ωc:=R3∖Ω¯. In the so‐called direct problem, the magnetic field B and the electric field E are unknown and are driven by a given incompressible flow field w. After eliminating E, a vector and a scalar potential ansatz for B in the interior and exterior domains, respectively, are applied, leading to a coupled interface problem. We apply a finite element approach in the bounded interior domain Ω, whereas a symmetric boundary element approach in the unbounded exterior domain Ωc is used. We present results on the well‐posedness of the continuous coupled variational formulation, prove the well‐posedness and stability of the semi‐discretized and fully discretized schemes, and provide quasi‐optimal error estimates for the fully discretized scheme. Copyright © 2013 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.2991