Multiphysics Discontinuous Galerkin Method And Posteriori Error Estimate For A Poroelasticity Model

In this paper, we propose a multiphysics discontinuous Galerkin method for a poroe-lasticity model. We reconstructed the original model by introducing the new variables and use the fully discrete multiphysics discontinuous Galerkin method to decouple the refor-mulated 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. This method overcomes the "locking phenomenon" which exhibits in the process of solving the poroelasticity model by the finite element method, and the numerical solution satisfies the conservation.And we derive the error estimates in the energy norm and give the numerical examples to confirm the theoretical results. What's more, we derive a new error indicator based on the multiphysics discontinuous Galerkin method for a poroelasticity model, we give the boundedness of the error indicator and present the numerical example to verify the convergence of the numerical solution.