Weak Galerkin finite element method for linear poroelasticity problems

Abstract: 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.