TY - JOUR
T1 - Multirate Time Iterative Scheme with Multiphysics Finite Element Method for a Nonlinear Poroelasticity
AU - Ge , Zhihao
AU - Li , Hairun
AU - Li , Tingting
JO - Journal of Computational Mathematics
VL - 2
SP - 597
EP - 616
PY - 2024
DA - 2024/01
SN - 42
DO - http://doi.org/10.4208/jcm.2207-m2021-0373
UR - https://global-sci.org/intro/article_detail/jcm/22893.html
KW - Nonlinear poroelasticity model, Multiphysics finite element method, Multirate
iterative scheme.
AB - <p style="text-align: justify;">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.</p>