Abstract In this paper, a fully discrete scheme of the fully dynamic Biot's model problem is proposed, which is constructed by using interior penalty discontinuous Galerkin method for the spatial approximation and a tailor difference scheme to approximate the first and second order temporal derivative terms. First of all, we prove the existence and uniqueness of solutions of proposed fully discrete scheme in proper norms. Then, based on the error equations a priori error estimates shall be derived for both primal variables displacement and pore pressure. Finally, a series of numerical examples are given to examine the convergence results by using the proposed numerical scheme to solve the fully dynamic Biot's model problem.

中文翻译：

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全动态 Biot 模型的不连续 Galerkin 方法

摘要 本文提出了一种全动态Biot模型问题的全离散方案，该方案采用内罚不连续Galerkin方法进行空间逼近，采用剪裁差分方案逼近一阶和二阶时间导数项。首先，我们证明了所提出的完全离散方案在适当范数下的解的存在性和唯一性。然后，基于误差方程，可以推导出原始变量位移和孔隙压力的先验误差估计。最后，给出了一系列数值例子来检验使用所提出的数值方案解决全动态Biot模型问题的收敛结果。