In this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the analysis of Hybrid High-Order (HHO) schemes. A relevant feature of the proposed framework is that it rests on mild time regularity assumptions that can be derived from an appropriate weak formulation of the continuous problem. To the best of our knowledge, these regularity results for the Biot problem are new. A novel family of HHO discretisation schemes is also proposed and analysed, and their performance numerically evaluated.

中文翻译：

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多孔弹性整体离散化的抽象分析框架及其在混合高阶方法中的应用

在这项工作中，我们为多孔弹性问题的完全耦合离散化的稳定性和收敛性分析引入了一种新颖的抽象框架，并将其应用于混合高阶（HHO）方案的分析。拟议框架的一个相关特征是，它基于温和的时间规律性假设，这些假设可以从对连续问题的适当弱公式中得出。据我们所知，关于毕奥问题的这些规律性结果是新的。还提出并分析了新颖的HHO离散化方案系列，并对它们的性能进行了数值评估。