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Analysis of a kinematic dynamo model with FEM–BEM coupling
Author(s) -
Lemster W.,
Lube G.,
Of G.,
Steinbach O.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2991
Subject(s) - mathematics , discretization , finite element method , dynamo , bounded function , mathematical analysis , ansatz , scalar (mathematics) , domain (mathematical analysis) , boundary (topology) , coupling (piping) , scalar field , geometry , magnetic field , physics , mathematical physics , quantum mechanics , engineering , thermodynamics , mechanical engineering
We consider a kinematic dynamo model in a bounded interior simply connected region Ω and in an insulating exterior region Ω c : = R 3 ∖ 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 Ω c 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.