A Penalty-Free or Penalty-Factor-Free DG Method with a Locally Reconstructed Curl Operator for the Maxwell Eigenproblem (Communications in Computational Physics, 2025)
A new discontinuous Galerkin (DG) method is proposed and analyzed forthe Maxwell eigenproblem, featuring a local reconstruction of the curl operator ina discontinuous finite element space. The proposed method can be penalty-free orpenalty-factor-free, depending on which discontinuous finite element space the curloperator is locally reconstructed in. The new DG method is recast into a saddle-point problem so that it can be analyzed from the Babuška-Osborn theory for the finite element approximation of the spectrum of the compact operator, and the convergence and the optimal error estimates are then obtained; the discrete eigenmodesare spurious-free and spectral-correct. We provide numerical results to illustrate theproposed method.
Keywords: Maxwell eigenproblem; discontinuous Galerkin finite element method; local reconstruction; curl operator; convergence; error estimates.