Multirate iterative scheme based on multiphysics discontinuous Galerkin method for a poroelasticity model

In the paper, we propose a multirate iterative scheme based on multiphysics discontinuous Galerkin method for a poroelasticity model. We solve a generalized Stokes problem in the coarse time size and solve the diffusion problem in the finer time size, and use the multiphysics discontinuous Galerkin method for the discretization of the space variables. And we prove that the multirate iterative scheme is stable and the numerical solution satisfies some energy conservation laws. Also, we prove that the convergence order is optimal in the energy norm. Finally, we give the numerical tests to verify that the multirate iterative scheme not only greatly reduces the computational cost, but also has no “locking phenomenon”.