A novel field-based mixed formulation of magnetostatics

A mixed variational formulation in 2-D magnetostatics is presented and discussed. The method treats B and H as direct unknowns and relies on the minimization of the error on the constitutive law, taking Maxwell's equations as constraints. The numerical discretization, based on the lowest order Raviart-Thomas-Nedelec element, is reported. The potential advantages of this innovative method for engineering applications-like the fulfilment of continuity equations-are pointed out and a case study is presented. A computer code has been implemented and a number of numerical experiments have been performed to validate the proposed methodology.