Istituto di Matematica Applicata e Tecnologie Informatiche     
Alotto P., Perugia I. A field-based finite element method for magnetostatics derived from an error minimisation approach. Preprint ercim.cnr.ian//1998-1102, 1998.
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 consists in minimising the residual of the constitutive equation under constraints represented by Maxwell's equations, which are exactly imposed with Lagrange multipliers. The most natural finite elements for both the magnetic and the magnetic induction fields are used in the numerical approximation to overcome the unsatisfactory behaviour of potential--based formulations in the neighbourhood of sharp discontinuities in material properties. Also, conditions under which the formulation can be decomposed in two separate sets of equations are discussed, 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.
Subject Magnetostatics, numerical approximations

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