We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model, and we develop a stability analysis in the continuous setting that holds both for the full inertial and quasi-static problems and that is robust with respect to most of the physical parameters of the problem. For spatial discretization, we propose an arbitrary-order weighted symmetric interior penalty scheme that supports general polytopal grids and is robust with respect to strong heterogeneities in the model coefficients. For the semi-discrete problem, we prove the extension of the stability result demonstrated in the continuous setting. A wide set of numerical simulations is presented to assess the convergence and robustness properties of the proposed method. Moreover, we test the scheme with literature and physically sound test cases for proof-of-concept applications in the geophysical context.

翻译：我们提出并分析了一种用于开尔文-沃伊特热/多孔粘弹性问题数值模拟的间断伽辽金方法。我们给出了模型的推导过程，并在连续框架下建立了稳定性分析，该分析同时适用于完全惯性问题和准静态问题，并且对问题中的大多数物理参数具有鲁棒性。对于空间离散化，我们提出了一种任意阶加权对称内部惩罚格式，该格式支持一般多面体网格，并对模型系数中的强异质性具有鲁棒性。针对半离散问题，我们证明了连续框架中稳定性结果的扩展性。通过大量数值模拟评估了所提方法的收敛性和鲁棒性。此外，我们采用文献中的案例和物理意义明确的测试算例对该格式进行了验证，以展示其在地球物理背景下的概念验证应用。