Ungauged Formulations and Current Conservation
Current conservation is inherent in Ampère’s law and it is known that if current is conserved, explicit gauge fixing is not necessary as iterative solvers converge toward a valid solution. However, it is generally not sufficient for the source currents to be divergence free in an analytical sense as when interpolated on the finite element functional basis, this property is not conserved.
When using the Magnetic and Electric Fields interface the electric potential is used to state current conservation so unless nonphysical current sources are specified inside the computational domain current conservation is fulfilled.
When using the Magnetic Fields interface, current conservation is usually imposed either by the solver (for magnetostatics) or in the transient or time harmonic case by the induced current density. The explicit gauge or divergence constraint can also help imposing current conservation as described in
Explicit Gauge Fixing/Divergence Constraint
.