Regularized Maxwell Equations and Nodal Finite Elements for Electromagnetic Field Computations

This article presents an alternative approach to the usual finite element formulation based on edge elements and double-curl Maxwell equations. This alternative approach is based on nodal elements and regularized Maxwell equations. The advantage is that, without adding extra unknowns (such as Lagrange multipliers), it provides spurious-free solutions and well-conditioned matrices. The drawback is that a globally wrong solution is obtained when the electromagnetic field has a singularity in the problem domain. The main objective of this work is to obtain accurate solutions with nodal elements and the regularized formulation, even in the presence of electromagnetic field singularities.