A mixed-FEM and BEM coupling for a two-dimensional eddy current problem

We study in this paper the electromagnetic field generated in an infinite cylindrical conductor by an alternating current density. The resulting interface problem (see [1]) between the metal and the dielectric medium is treated by a mixed-FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and leads to a convergent Galerkin method with optimal error estimates. Furthermore, we introduce a fully discrete version of our Galerkin scheme based on simple quadrature formulas. We show that, if the parameter of discretization is sufficiently small, the fully discrete method is well posed and the error estimates remain unaltered.