In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the original equation as a system of first order differential equations we introduce the method and show that the resulting discrete formulation is well-posed, stable and retains super-optimal rate of convergence with respect to the discretization parameters, namely the time step and the polynomial approximation degree. A set of two- and three-dimensional numerical experiments confirm the theoretical bounds. Finally, the method is applied to real geophysical applications.

翻译：在这项工作中,我们为二阶差差分系统提出了一个新的高顺序、不连续的加列金时间整合计划,该计划通常产生于 Elasto动力学方程式的空间离散。通过将原始方程式改写为一阶差分方程式系统,我们引入了这种方法,并表明由此产生的离散方程式在离散参数(即时间步骤和多维近似度)方面位置良好、稳定并保持超优的趋同率。一套二维和三维数字实验证实了理论界限。最后,该方法适用于实际地球物理应用。