HEJ, HU ISSN 1418-7108 Manuscript no.: ANM-981030-A

   
Conclusions

We have established mixed variational formulations for linear and nonlinear three-dimensional static electro-magnetic field problems. We have shown that the formulation in the space ${\bf Y}= H_0({ \bf rot };\Omega) \cap H(\div ;\Omega)$ represents the magnetostatic problem well. The analysis shows that the both the linear and the nonlinear problem have a unique solution. Further, the solution for the Lagrange multiplier $\lambda$ is equal to zero. Thus, the solution for the variable ${\bf u}$ (in which we are interested only) can be obtained by solving a coercive formulation not involving the unknown $\lambda$.

HEJ, HU ISSN 1418-7108 Manuscript no.: ANM-981030-A