Complementary hybrid formulations for 2D magnetostatics

Hybrid b- and h-formulations for the solution of the 2D magnetostatic problem are presented. These formulations can be written in such a way that the resulting system matrices are identical up to the coefficient related to the material properties. Thus after the evaluation of the required matrix terms two complementary solutions of the problem are obtained easily with the total computational cost of almost one. The complementarity of the solutions gives a good basis for the adaptive mesh refinement. In the derivation of the formulations differential forms, which best describe the underlying idea, have been used.