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Volume 42, Issue 2
Multirate Time Iterative Scheme with Multiphysics Finite Element Method for a Nonlinear Poroelasticity

Zhihao Ge, Hairun Li & Tingting Li

DOI: 10.4208/jcm.2207-m2021-0373

J. Comp. Math., 42 (2024), pp. 597-616.

Published online: 2024-01

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  • Abstract

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.

  • Keywords

Nonlinear poroelasticity model, Multiphysics finite element method, Multirate iterative scheme.

  • AMS Subject Headings

65N30, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-597, author = {Ge , ZhihaoLi , Hairun and Li , Tingting}, title = {Multirate Time Iterative Scheme with Multiphysics Finite Element Method for a Nonlinear Poroelasticity}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {2}, pages = {597--616}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2207-m2021-0373}, url = {http://global-sci.org/intro/article_detail/jcm/22893.html} }
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 -

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.

Zhihao Ge, Hairun Li & Tingting Li. (2024). Multirate Time Iterative Scheme with Multiphysics Finite Element Method for a Nonlinear Poroelasticity. Journal of Computational Mathematics. 42 (2). 597-616. doi:10.4208/jcm.2207-m2021-0373
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