Enforcing interface field continuity to advance finite element approximations in heterogeneous materials

To investigate the discrete field continuity at the interface of inhomogeneous materials, this paper investigates the scattering of electromagnetic waves interacting with a perfect electrical conductor object coated with dielectric materials, employing the finite element method. In the derivation process of the variational formulation, the tangential continuity of electric fields eliminates any discrepancies occurring along the internal interfaces. However, while it is important to maintain tangential continuity of electric and magnetic fields at the interface between different dielectrics, this requirement is not met precisely within discrete space. As a result, approximations can exhibit inaccuracies and potentially fail to fully capture the underlying physical phenomena. To alleviate these issues, we propose an imposition of tangential continuity of the magnetic field within the minimizing functional, thereby ensuring adherence to interface conditions between two dielectric layers. This approach can be naturally applied to a variety of interface problems to enhance the approximation accuracy of interaction models in real-world environments.