  This paper is devoted to a weak Galerkin (WG) finite element method for
linear poroelasticity problems where weakly defined divergence and gradient
operators 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 an $H^1$
type and $L^2$ norms for the pressure. Finally, numerical experiments are
presented to illustrate the theoretical error results in different kinds of
meshes which shows the WG flexibility for mesh selections, and to verify the
locking-free property of our proposed method.
