Weak Galerkin finite element method for linear poroelasticity problems

In this paper, we develop a weak Galerkin (WG) finite element method for a linear poroelasticity model where weak divergence and weak gradient operators defined over discontinuous functions are introduced. We establish both the continuous and discrete time WG schemes, and obtain their optimal convergence order estimates in a discrete $H^1$ norm for the displacement and in $H^1$ and $L^2$ norms for the pressure. Finally, we present some numerical experiments on different kinds of meshes to illustrate the theoretical error results, and furthermore verify the locking-free property of our proposed method.