A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations

Let Ω ⊂ R2 be a bounded polygonal domain, f ∈ [L2(Ω)]2, and k ≥ 0. Consider the time-harmonic Maxwell equations with the perfectly conduct-ing boundary condition: Find u ∈ H0(curl; Ω) such that (1) (∇ × u,∇ × v) − k2(u,v) = (f,v) for allv ∈ H0(curl; Ω)