A functional for dynamic finite-element solutions in electromagnetics

A new functional is introduced that satisfies of Maxwell's equations, provi des minimization, and eliminates spurious solutions. An analytical method i s developed that provides a means of evaluating functional forms. The analy tical method confirms the effective functional form as the fundamental caus e underlying the difficulties with spurious solutions that are not complete ly eliminated under all circumstances, It is shown that the curl-curl "func tional" form allows for the existence of an improper gradient behavior in a general field expansion. The new functional is shown to be self adjoint an d positive definite, thus providing an error minimization, Numerical result s are obtained that demonstrate the effectiveness of the new functional to prevent spurious solutions using node-based elements.