On the coupling of LDG-FEM and BEM methods for the three dimensional magnetostatic problem

We present two new coupling models for the three dimensional magnetostatic problem. In the first model, we propose a new coupled formulation, prove that it is well posed and solves Maxwell’s equations in the whole space. In the second, we propose a new coupled formulation for the Local Discontinuous Galerkin method, the finite element method and the boundary element method. This formulation is obtained by coupling the LDG method inside a bounded domain Ω1 with the FEM method inside a layer Ω2≔Ω⧹Ω¯1 where Ω is a bounded domain which is made up of material of permeability μ   and such that Ω¯1⊂Ω, and with a boundary element method involving Calderon’s equations. We prove that our formulation is consistent and well posed and we present some a priori error estimates for the method.