APPROXIMATION OF THE EIGENVALUE PROBLEM FOR THE TIME HARMONIC MAXWELL SYSTEM BY CONTINUOUS LAGRANGE FINITE ELEMENTS Academic Article

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:blackconsidering a mixed method/span controlling the divergence of the electric field in a fractional Sobolev space H H^{-alpha } with ( 1 2 , 1 ) alpha in (frac 12,1) . The method is shown to be convergent and spectrally correct.