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 d eveloped 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 constra ints represented by Maxwell's equations, which are exactly imposed with Lag range multipliers. In order to obtain computed fields with correct continui ty properties across interfaces between materials with different permeabili ty, the magnetic and the magnetic induction fields are used in a complement ary way, and discretized by edge and face elements. Moreover, it is discuss ed how the formulation can be decomposed into two separate sets of equation s, highlighting the relationship with classical formulations. A preconditio ned iterative scheme to solve the final algebraic linear system is also pre sented. Furthermore, a very natural refinement indicator is defined to guid e an adaptive mesh refinement procedure. Copyright (C) 2000 John Wiley & So ns, Ltd.