On the Equivalence of Finite Element and Finite Integration Formulations

The paper offers a comparative study of numerical methods of analysis of electromagnetic fields. The focus is on the finite element method (FEM) and finite integration technique (FIT), but with the cell and equivalent network approaches also considered. It is shown how the approximate integrals describing coefficients of the FEM need to be derived for a mesh with parallelepiped elements to achieve consistency with FIT equations. The equivalence of FEM and FIT formulations for a triangular mesh in 2D is highlighted. The TEAM Workshops Problem No. 7 is used as an example for numerical comparisons. Two formulations have been considered: 1) using the edge values of the magnetic vector potential A and the nodal values of the electric scalar potential V; and 2) expressed in terms of the edge values of both magnetic A and electric T-T₀ vector potentials.