Fully Discrete Equal-order Mixed Finite Element Method For A Poroelasticity Model

In the paper, we consider a quasi-static poroelasticity model. To reveal the multi-physical process of deformation and diffusion for poroelastic materials, we firstly refor-mulate the original model into a diffusion equation coupled with a generalized Stokes problem. We then propose a time-stepping algorithm which decouples the reformulated problem at each time step, and contains the constraint condition ?t ? O(h2). After that we propose a fully-discrete lowest equal-order stabilized mixed finite element method for the reformulated model to overcome the "locking" phenomenon and reveal the multi-physical process. We prove that the mandatory condition holds and the method has the optimal order error estimates. Then, we give another coupling algorithm, and the time using Crank-Nicolson format. We have proved the error estimate of the algorithm, and The results show that the time error is increased to the second order and the restriction condition ?t ? O(h2) is removed. Finally, we give numerical examples for each algorithm to verify the theoretical results.