标题： 耦合的孔隙粘弹性与热粘弹性系统的杂交间断Galerkin方法 显示英文标题

标题： Hybridizable Discontinuous Galerkin Methods for Coupled Poro-Viscoelastic and Thermo-Viscoelastic Systems

摘要： 本文提出了一种统一的数学框架，用于建模耦合的孔隙-黏弹性与热-黏弹性现象，并将其表述为一阶时间偏微分方程组。 该模型描述了固体速度、弹性和黏性应力张量以及与流体压力或温度相关的附加场的演化，具体取决于物理背景。 我们开发了一种混合化的间断伽辽金方法来数值逼近这个耦合系统，提供了一种高阶、稳定的离散化方案，能够高效处理问题的多物理特性。 我们进行了稳定性分析，并推导出半离散格式下的最优 $hp$-误差估计。 通过全面的数值实验验证了理论收敛率，展示了该方法在各种测试案例中的准确性与鲁棒性，包括具有混合黏弹性特性的非均匀介质中的波传播。 显示英文摘要

摘要： This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution of solid velocity, elastic and viscous stress tensors, and additional fields related to either fluid pressure or temperature, depending on the physical context. We develop a hybridizable discontinuous Galerkin method for the numerical approximation of this coupled system, providing a high-order, stable discretization that efficiently handles the multiphysics nature of the problem. We establish stability analysis and derive optimal $hp$-error estimates for the semi-discrete formulation. The theoretical convergence rates are validated through comprehensive numerical experiments, demonstrating the method's accuracy and robustness across various test cases, including wave propagation in heterogeneous media with mixed viscoelastic properties.