In 2D axisymmetric formulation using vector field such as the magnetic vector potential, it is beneficial to formulate the out-of-plane dependent variable as Ψ = rAϕ, referred to as the covariant formulation. The covariant formulation has better performance in terms of numerical stability and accuracy. Moreover, the covariant dependent variable usually has a physical meaning, for instance, the difference Ψ between two magnetic surfaces is equal to the poloidal magnetic flux per radian.

One of the advantages of Ψ formulation is that for linear discretization it gives more accurate results than that with The A Formulation. However, using linear discretization is not recommended since the magnetic field is zero at the axis. Always perform a mesh adaptation study to make sure the results are not mesh dependent when linear discretization is used.