Abstract In the paper, a new lowest equal-order stabilized mixed finite element method is proposed for a poroelasticity model in displacement-pressure formulation, which is based on multiphysics approach. The original model is reformulated to reveal the multi-physical process of deformation and diffusion and get a coupled fluid system. Then, a time-stepping algorithm which decouples the reformulated problem at each time step and the lowest equal-order stabilized mixed finite element method for the reformulated problem is given, which can overcome the “locking” phenomenon. Also, the stability analysis and error analysis are proved that the stabilized mixed finite element method is stable for the pair of finite elements without the inf-sup condition and has the optimal convergence order. Finally, the numerical examples are shown to verify the theoretical results, and a conclusion is drawn to summarize the main results in this paper.

中文翻译：

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基于多物理场方法的多孔弹性模型最低等阶稳定混合有限元方法

摘要 在本文中，基于多物理场方法，提出了一种新的最低等阶稳定混合有限元方法，用于位移-压力公式中的多孔弹性模型。重构原始模型以揭示变形和扩散的多物理过程并得到耦合流体系统。然后，给出了在每个时间步解耦重构问题的时间步长算法和重构问题的最低等阶稳定混合有限元方法，可以克服“锁定”现象。稳定性分析和误差分析证明了稳定混合有限元法对于没有inf-sup条件的有限元对是稳定的，具有最优收敛阶数。最后，