Mixed and hybrid formulations for the three‐dimensional magnetostatic problem

We propose mixed and hybrid formulations for the three‐dimensional magnetostatic problem. Such formulations are obtained by coupling finite element method inside the magnetic materials with a boundary element method. We present a formulation where the magnetic field is the state variable and the boundary approach uses a scalar Dirichlet‐Neumann map to describe the exterior domain. Also, we propose a second formulation where the magnetic induction is the state variable and a vectorial Dirichlet‐Neumann map is used to describe the outer field. Numerical discretizations with “edge” and “face” elements are proposed, and for each discrete problem we study an “inf‐sup” condition. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 85–104, 2002