Abstract
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 Omega(1) with the FEM method inside a layer Omega(2) := Omega \ (Omega(1)) over bar where Omega is a bounded domain which is made up of material of permeability l and such that (Omega(1)) over bar subset of Omega, 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. (C) 2010 Elsevier Inc. All rights reserved.