We present an arbitrary high-order local discontinuous Galerkin (LDG) method with alternating fluxes for solving linear elastodynamics problems in isotropic media. Both the semi-discrete analysis and fully discrete analysis for a leap-frog LDG method are given to show that the proposed method simultaneously enjoys the energy conserving property and optimal convergence rates in both the displacement and stress, when the tensor product polynomials of the degree k are used on Cartesian meshes. Numerical experiments demonstrate that the proposed method has several advantages including the exact energy conservation, slow-growing errors in long time simulation, and subtle dependence on the first Lamé parameter \(\lambda \).

我们提出了一种具有交替通量的任意高阶局部不连续Galerkin（LDG）方法，用于解决各向同性介质中的线性弹性动力学问题。给出了跨越式LDG方法的半离散分析和完全离散分析，结果表明，当该张量积多项式等于0时，该方法在位移和应力上同时具有节能特性和最优收敛速度。k用于笛卡尔网格。数值实验表明，该方法具有精确的能量守恒，长时间仿真中的缓慢增长误差以及对第一Lamé参数\（\ lambda \）的微妙依赖等优点。