Analysis of a Weak Galerkin Mixed Formulation for Modified Maxwell’s Equations

Abstract

In this paper, we are interested in studying a mixed formulation of weak Galerkin type to approach the electric field and a Lagrange multiplier, which are solutions of a problem deriving from Maxwell’s equations. Our numerical scheme is formed with stable finite elements constructed of usual polynomials of degree k for the electric field and of degree k+1 for the Lagrange multiplier; its consistency and well-posedness are shown. Some optimal error estimates are proven and tested numerically in a bounded subdomain of R2.