A comparative study of magnetostatics using three-field and conventional vector potential formulations

The three-field finite element formulation for electromagnetics was proposed as an alternative to the existing vector potential formulations. In the formulation, three fields, that is (i) the vector potential, (ii) the divergence of the vector potential and (iii) a scalar variable which is adjoint to (ii), are interpolated independently and the imposition of the gauge condition can be relaxed. A comparative study of magnetostatic problems is presented which includes the calculations by conventional vector potential formulations using second order nodal elements. It is shown that the three-field formulation gives better results than conventional vector potential formulations with and without gauging.