Primal dual weak Galerkin finite element method for Maxwells' equations

This work proposes and analyzes a numerical scheme for time-harmonic Maxwell's equations using the Primal-Dual Weak Galerkin Finite Element Method (PDWG-FEM). The resulting Euler Lagrange Equation offers a symmetric finite element scheme involving primal and dual variables. The error estimate of the optimal order is estimated for the corresponding numerical solution in discrete Sobolev norms, including $ L^2 $ topology. The Numerical experiments are presented for the 2-dimensional case using MATLAB software to illustrate and confirm the theory developed for the PDWG-FEM method.