The role of the penalty in the local discontinuous Galerkin method for Maxwell’s eigenvalue problem

Abstract

The local discontinuous Galerkin (LDG) method is a promising emerging technology for discretizing a wide range of differential operators. It is well known that the robustness of this method is contingent upon a stabilization term. We analyze the role of this term in the LDG discretization of the Maxwell curl–curl operator, demonstrating that the stabilization parameter can be used to split the spectrum into two sections. The first set of eigenvalues approximate the spectrum of the curl-conforming finite element curl–curl operator, while the second set are spurious eigenvalues that can be made arbitrarily large by increasing the stabilization parameter. We confirm this analysis with a range of computational experiments that compare the spectra obtained from LDG and curl-conforming discretizations.