Multirate Iterative Scheme And Posteriori Error Estimate For A Poroelasticity Model

In the paper,we propose a multirate iterative scheme based on multiphysics finite element method and give a new posteriori error analysis based on multirate iterative scheme for a poroelasticity model.Firstly,we reformulate the original model to fluid coupled.Then,we use the multiphysics finite element method for the discretization of the space variables and adopt a multirate iterative scheme on the time scale which solve a generalized Stokes problem in the coarse time size and solve the diffusion problem in the finer time size.And we prove that the multirate iterative scheme is stable and the numerical solution satisfies the energy conservation law.Also,we prove that it doesn't reduce the precision of numerical solution and greatly reduces the computational cost.Meanwhile,we give the numerical tests to verify the theoretical result.Next,we propose some new error estimators based on multirate iterative scheme.The proposed error estimators are demonstrated to be computationally very efficient and give a posteriori error estimate.Finally,we present numerical examples to verify and validate the efficiency of applying the proposed error estimators in adaptive mesh.It has been clearly shown that the adaptive scheme can reduce the computational cost and overcome the “locking phenomenon”.