In this work we present a new high order space-time discretization method based on a discontinuous Galerkin paradigm for the second order visco-elastodynamics equation. After introducing the method, we show that the resulting space-time discontinuous Galerkin formulation is well-posed, stable and retains optimal rate of convergence with respect to the discretization parameters, namely the mesh size and the polynomial approximation degree. A set of two and three-dimensional numerical experiments confirms the theoretical bounds.

中文翻译：

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弹性波方程的时空不连续Galerkin方法

在这项工作中，我们提出了一种新的基于不连续Galerkin范式的高阶时空离散方法，用于二阶粘弹性动力学方程。引入该方法后，我们表明，所得的时空不连续Galerkin公式相对于离散化参数（即网格大小和多项式逼近度）具有良好的定位性，稳定性，并保留了最佳收敛速度。一组二维和三维数值实验确定了理论界限。