(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, we study a new finite element method for poroelasticity problem with homogeneous boundary conditions. The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity, i.e., the stress tensor, displacement and pressure are unknown variables in the weak form. For the linear elasticity formula, we use a conforming finite element proposed in [11] for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow. We will show that the newly proposed finite element method maintains optimal convergence order.