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

An enhanced version of a mixed field-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 Maxwell's equations, which are exactly imposed with Lagrange multipliers. In order to obtain computed fields with correct continuity properties across interfaces between materials with different permeability, the magnetic and the magnetic induction fields 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 final algebraic linear system is also presented. Furthermore, a very natural refinement indicator is defined to guide an adaptive mesh refinement procedure.