论文标题
对于Biot的模型，一种非对称方法以及准最佳和鲁棒的离散化。第一部分 - 理论方面
A nonsymmetric approach and a quasi-optimal and robust discretization for the Biot's model. Part I -- Theoretical aspects
论文作者
论文摘要
我们考虑了通过向后的Euler方案的两场配方的时间离散化的偏微分方程系统。在此问题的空间离散化中遇到的典型困难是相对于各种材料参数的鲁棒性。我们通过观察到合适的非对称变化环境中的所有参数，无论所有参数如何，我们都可以通过观察该问题均匀稳定来处理这个问题。在此结果的指导下，我们设计了一种新型的不合格离散化，该离散化采用了Crouzeix-Raviart和不连续的元素。我们证明，在参数依赖性规范中，提出的离散化是准最佳和鲁棒的，并讨论了该结果的后果。
We consider the system of partial differential equations stemming from the time discretization of the two-field formulation of the Biot's model with the backward Euler scheme. A typical difficulty encountered in the space discretization of this problem is the robustness with respect to various material parameters. We deal with this issue by observing that the problem is uniformly stable, irrespective of all parameters, in a suitable nonsymmetric variational setting. Guided by this result, we design a novel nonconforming discretization, which employs Crouzeix-Raviart and discontinuous elements. We prove that the proposed discretization is quasi-optimal and robust in a parameter-dependent norm and discuss the consequences of this result.
