Generalized Cartesian finite elements

This paper presents a new family of vectorial expansion functions that can accurately and consistently model the behavior of the electric and the magnetic field strengths both at interfaces between media with different constitutive parameters and inside interface-free subdomains. This new family of expansion functions is constructed by suitably connecting local Cartesian (nodal) expansion functions that may be of any order. The accuracy obtained by using first-order expansion functions in a finite-element code is demonstrated by solving a problem with a known analytical solution.