On a finite-element method for solving the three-dimensional maxwell equations

The aim of this paper is to present a method for solving the time-domain three-dimensional Maxwell equations, which can be coupled with a particle solver. For this purpose, Maxwell's equations are reformulated as a constrained wave equation system, with Lagrange multipliers associated to the conditions Δ · B - 0 and Δ · E - ρ/ϵ₀. We approximate both the fields and the Lagrange multipliers with a finite element method using a Taylor Hood element.