Coupling of local and global quantities in various finite element formulations and its application to electrostatics, magnetostatics and magnetodynamics

A method for defining global quantities related to fluxes and circulations is proposed in the frame of the finite element method. The definition is in perfect accordance with the discretized weak formulations of the problems. It therefore enables a natural coupling between local and global quantities in various formulations, while keeping a symmetrical matrix for the system, and then is open to the coupling of physical problems. Applications are given for electrostatics, magnetostatics and magnetodynamics.