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

Abstract

We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H 1 \mathbf {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^{-\alpha } with α ∈ ( 1 2 , 1 ) \alpha \in (\frac 12,1) . The method is shown to be convergent and spectrally correct.