An H-based FEM-BEM formulation for a time dependent eddy current problem

In this paper, we study a time-dependent eddy current problem posed in the whole space. We prove that the problem has a well-posed weak formulation. We also show that the latter formulation admits a well-posed saddle point structure when the constraint satisfied by the magnetic field in the dielectric medium is handled by means of a Lagrange multiplier. Furthermore, we provide a BEM-FEM formulation of the problem that leads to a semi-discrete Galerkin scheme based on Nédélec's edge elements and Raviart–Thomas elements. Finally, we analyze the asymptotic behavior of the error in terms of the mesh size parameter.