A mixed formulation for 3D magnetostatic problems: theoretical analysis and face-edge finite element approximation

A mixed field-based variational formulation for the solution of threedimens ional magnetostatic problems is presented and analyzed. This method is base d upon the minimization of a functional related to the error in the constit utive magnetic relationship, while constraints represented by Maxwell's equ ations are imposed by means of Lagrange multipliers. In this way, both the magnetic field and the magnetic induction field can be approximated by usin g the most appropriate family of vector finite elements, and boundary condi tions can be imposed in a natural way. Moreover, this method is more suitab le than classical approaches for the approximation of problems featuring st rong discontinuities of the magnetic permeability, as is usually the case. A finite element discretization involving face and edge elements is also pr oposed, performing stability analysis and giving error estimates.