This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The mathematical model consists of the low-frequency Biot's equations in the poroelastic medium and the elastodynamics equation for the elastic one. To realize the coupling, suitable transmission conditions on the interface between the two domains are (weakly) embedded in the formulation. The proposed PolydG discretization in space is then coupled with a dG time integration scheme, resulting in a full space-time dG discretization. We present the stability analysis for both the continuous and the semidiscrete formulations, and we derive error estimates for the semidiscrete formulation in a suitable energy norm. The method is applied to a wide set of numerical test cases to verify the theoretical bounds. Examples of physical interest are also presented to investigate the capability of the proposed method in relevant geophysical scenarios.

翻译：本文针对耦合多孔弹性-弹性介质中波传播的数值离散问题，研究了一种基于多面体网格的时空有限元间断伽辽金方法（XT-PolydG）。数学模型由多孔弹性介质中的低频Biot方程与弹性介质中的弹性动力学方程组成。为实现耦合，通过（弱）嵌入方式将两域界面的合适传输条件纳入公式。提出的空间PolydG离散化与时间dG积分格式相结合，形成完整的时空dG离散化。我们分析了连续形式和半离散形式的稳定性，并在合适的能量范数下推导了半离散形式的误差估计。将该方法应用于大量数值算例以验证理论界值，同时展示物理实例以探究该方法在地球物理相关场景中的能力。