We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and $hp$-version error estimates in suitable energy norms are derived for the semi-discrete problem. The fully-discrete scheme is then obtained based on employing an implicit Newmark-$\beta$ time integration scheme. A wide set of numerical simulations is reported, both for the verification of the theoretical estimates and for examples of physical interest. A comparison with the results of the poroelastic model is provided too, highlighting the differences between the predictive capabilities of the two models.

翻译：本文提出并分析了一种适用于热-孔隙弹性介质中波传播模型空间离散的高阶间断伽辽金方法。该方案支持一般多面体网格。针对半离散问题，推导了稳定性分析及合适的能量范数下的$hp$版本误差估计。通过采用隐式Newmark-$\beta$时间积分格式，进一步得到全离散方案。报告了广泛数值模拟结果，既包括理论估计的验证，也涵盖具有物理意义的算例。同时与孔隙弹性模型的结果进行了对比，凸显了两种模型预测能力之间的差异。