Comparison of full and reduced potential formulations for low-frequency applications

The authors examine five alternative finite element formulations of magnetostatic problems: (1) full vector potential, (2) reduced vector potential, (3) reduced scalar potential with source integral over all volume, (4) reduced scalar potential with source integral over permeable volumes only, and (5) reduced scalar potential with surface source integral. They show that (3) is more prone to numerical errors than the other methods, and that (4) and (5) are competitive in accuracy with (1) and (2) in air regions but are easier to implement in three dimensions. However, all three scalar formulations suffer from cancellation errors in iron regions