Multiphysics discontinuous Galerkin method for a poroelasticity model

In this paper, we develop and analyze a multiphysics discontinuous Galerkin method for a poroelasticity model, which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. And we prove that the multiphysics discontinuous Galerkin method is absolutely stable for all positive mesh size h. Also, we propose a time-stepping algorithm which decouples the reformulated poroelasticity model at each time step into two sub-problems, one of which is a generalized Stokes problem for the displacement vector field along with a pseudo-pressure and the other is a diffusion problem for the pseudo-pressure field. And we give the optimal order error estimates in the energy norm. Finally, we give the numerical examples to verify the theoretical results.