(untitled) (Journal of Computational Mathematics, 2024)
In this paper, a multirate time iterative scheme with multiphysics finite element method is proposed and analyzed for the nonlinear poroelasticity model. The original problem is reformulated into a generalized nonlinear Stokes problem coupled with a diffusion problem of a pseudo pressure field by a new multiphysics approach. A multiphysics finite element method is adopted for the spatial discretization, and the generalized nonlinear Stokes problem is solved in a coarse time step and the diffusion problem is solved in a finer time step. The proposed algorithm is a decoupled algorithm, which is easily implemented in computation and reduces greatly computation cost. The stability analysis and the convergence analysis for the multirate iterative scheme with multiphysics finite element method are given. Some numerical tests are shown to demonstrate and validate the analysis results.