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.

翻译：我们提出间断伽辽金（DG）方法，用于求解一阶半线性双曲系统，该系统最初被提出作为一维拓扑谐振子二聚体晶格的连续模型。我们研究了与简单、网格无关数值通量选择相关的能量守恒或能量耗散特性。我们证明，在特定数值通量选择下，我们的DG方法在$L^2$范数下实现了最优收敛。我们提供了数值实验，验证并展示了所提数值方法的有效性。