A lowest equal-order stabilized mixed finite element method based on multiphysics approach for a poroelasticity model

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.