Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H 1 H^1 -conforming finite elements. The key idea consists of 󠀼span style=󠀢color:black󠀢󠀾considering a mixed method󠀼/span󠀾 controlling the divergence of the electric field in a fractional Sobolev space H − α H-α with α ∈ ( 1 2 , 1 ) α ∈ ( 12,1) . The method is shown to be convergent and spectrally correct.