A field-based finite element method for magnetostatics derived from an error minimization approach

An enhanced version of a mixed eld-based formulation for magnetostatics developed in previous papers is presented under more general hypotheses and a deep discussion of its features is carried out. The approach relies upon the minimization of the residual of the constitutive equation under constraints represented by Maxwellʹs equations, which are exactly imposed with Lagrange multipliers. In order to obtain computed elds with correct continuity properties across interfaces between materials with di erent permeability, the magnetic and the magnetic induction elds are used in a complementary way, and discretized by edge and face elements. Moreover, it is discussed how the formulation can be decomposed into two separate sets of equations, highlighting the relationship with classical formulations. A preconditioned iterative scheme to solve the nal algebraic linear system is also presented. Furthermore, a very natural re nement indicator is de ned to guide an adaptive mesh re nement procedure