Study of a New Mixed Weak Galerkin Formulation for the Electric Field

In this paper, we present a new mixed weak Galerkin FEM for Maxwell’s equations in the primary electrostatic field–Lagrange multiplier. Our numerical scheme is equipped with stable finite elements composed of polynomials of degree ℓ for the electrostatic variable and polynomials of degree 𝓁+1 for the Lagrange multiplier variable; the electrostatic field and the Lagrange multiplier variables are discontinuous. We demonstrate some error estimations that are optimal as a function of the mesh size and we study some numerical tests in a 2D domain. The numerical results perfectly confirm those shown theoretically.