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 urn:x-wiley:1704214:media:mma2991:mma2991-math-0001. 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.