Ramiro Acevedo, Salim Meddahi:
An E-based mixed-FEM and BEM coupling for a time-dependent eddy current problem
In this paper, we analyze a mixed-FEM and BEM coupling for a time-dependent eddy current problem posed in the whole space and formulated in terms of the electric field E. The coupled problem is obtained by first proposing a mixed formulation of the interior problem in order to handle efficiently the divergence free constraint satisfied by E in the dielectric material. Next, we incorporate the far field effect to the latter formulation through boundary integral equations defined on the coupling interface. We show that the resulting degenerate parabolic problem (with saddle point structure) is well-posed and use Nedelec edge elements and standard nodal finite elements to define a semi-discrete Galerkin scheme. Furthermore, we introduce the corresponding backward-Euler fully-discrete formulation and analyze the asymptotic behavior of the error in terms of the discretization parameters for both schemes.