Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array

Abstract: We present discontinuous Galerkin (DG) methods for solving a first-order semi-linear hyperbolic system, which was originally proposed as a continuum model for a one-dimensional dimer lattice of topological resonators. We examine the energy-conserving or energy-dissipating property in relation to the choices of simple, mesh-independent numerical fluxes. We demonstrate that, with certain numerical flux choices, our DG method achieves optimal convergence in the $L^2$ norm. We provide numerical experiments that validate and illustrate the effectiveness of our proposed numerical methods.