A symmetric undifferentiated fully gauged T,Ψ-A-Ψ formulation

In the present paper a fully gauged T,Ψ-A-Ψ formulation for transient quasi-static 3D eddy current problems, in which the symmetry of the finite element system is achieved without differentiating in time any equation, is proposed. It is desirable to avoid such a differentiation, used in the literature to gain symmetry, because it is expected to produce finite element schemes safer against error growth, but leads to unsymmetrical matrices after discretization in space. Here, a technique proposed by the authors permits one to recover symmetry when discretizing in time. The differential model is carefully described and the way it incorporates the Coulomb gauge is discussed, as well as the existence and uniqueness of the solution. Comparisons with TEAM results are reported.