TY - JOUR
T1 - A Penalty-Free or Penalty-Factor-Free DG Method with a Locally Reconstructed Curl Operator for the Maxwell Eigenproblem
AU - Du , Zhijie
AU - Duan , Huoyuan
AU - Zhu , Duowei
JO - Communications in Computational Physics
VL - 3
SP - 887
EP - 922
PY - 2025
DA - 2025/08
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0151
UR - https://global-sci.org/intro/article_detail/cicp/24318.html
KW - Maxwell eigenproblem, discontinuous Galerkin finite element method, local reconstruction, curl operator, convergence, error estimates.
AB - <p style="text-align: justify;">A new discontinuous Galerkin (DG) method is proposed and analyzed for
the Maxwell eigenproblem, featuring a local reconstruction of the curl operator in
a discontinuous finite element space. The proposed method can be penalty-free or
penalty-factor-free, depending on which discontinuous finite element space the curl
operator 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 eigenmodes
are spurious-free and spectral-correct. We provide numerical results to illustrate the
proposed method.</p>