Multirate Time Iterative Scheme with Multiphysics Finite Element Method for a Nonlinear Poroelasticity (Journal of Computational Mathematics, 2024)
In this paper, a multirate time iterative scheme with multiphysics finite element methodis proposed and analyzed for the nonlinear poroelasticity model. The original problem isreformulated into a generalized nonlinear Stokes problem coupled with a diffusion problemof a pseudo pressure field by a new multiphysics approach. A multiphysics finite elementmethod is adopted for the spatial discretization, and the generalized nonlinear Stokesproblem is solved in a coarse time step and the diffusion problem is solved in a finertime step. The proposed algorithm is a decoupled algorithm, which is easily implementedin computation and reduces greatly computation cost. The stability analysis and theconvergence analysis for the multirate iterative scheme with multiphysics finite elementmethod are given. Some numerical tests are shown to demonstrate and validate the analysisresults.