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 coupled with a dG time integration scheme, resulting in a full space–time dG discretization. We present the stability analysis for both semidiscrete and fully discrete formulations, and derive error estimates in suitable energy norms. The method is applied to various 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.

中文翻译：

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耦合多孔弹性-弹性问题的间断伽辽金离散化


这项工作涉及在多面网格 （XT-PolydG） 上分析时空有限元间断伽辽金方法，用于耦合多孔弹性-弹性介质中波传播的数值离散化。数学模型由多孔弹性介质中的低频 Biot 方程和弹性介质的弹性动力学方程组成。为了实现耦合，两个域之间的界面上合适的传输条件被（弱地）嵌入到公式中。所提出的 PolydG 空间离散化与 dG 时间积分方案耦合，得到完整的空-时 dG 离散化。我们提出了半离散和全离散公式的稳定性分析，并在合适的能量范数中推导出误差估计。该方法应用于各种数值测试用例，以验证理论边界。还提出了物理兴趣的示例，以研究所提出的方法在相关地球物理场景中的能力。