Finite element modelling of electromagnetic fields using different types of variables and boundary conditions

The authors calculate the precision of the determinations of the magnetic field and current in a finite-element method when varying the size of the mesh, with two different types of boundary conditions (given electric field or given magnetic field) and three types of unknowns (nodal variables, one or two variables per edge). Precision for the determination of the current is shown to depend little on the types of variables and boundary conditions. One variable per edge is the better one. On the contrary, the precision for the magnetic field is greatly dependent on the types of variables and boundary conditions. One variable per edge gives very bad results. Nodal variables with h boundary conditions give the smallest errors; with e boundary conditions, two variables per edge is the better choice