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：本文研究了多面体网格上的时空有限元间断伽辽金方法（XT-PolydG）在耦合孔隙弹性-弹性介质中波传播数值离散问题。数学模型由孔隙弹性介质中的低频Biot方程和弹性介质中的弹性动力学方程组成。为实现耦合，通过在两个区域界面上（弱）嵌入合适的传输条件。所提出的空间PolydG离散化与dG时间积分方案耦合，形成完整的时空dG离散化。我们给出了连续和半离散公式的稳定性分析，并在合适的能量范数下推导了半离散公式的误差估计。该方法应用于广泛的数值测试案例以验证理论界限。还给出了具有物理意义的算例，以研究所提方法在相关地球物理场景中的能力。