Optimal Error Estimates of Multiphysics Finite Element Method for a Nonlinear Poroelasticity Model with Nonlinear Stress-Strain Relation

GE Zhi-hao, LI Hai-run, LI Ting-ting

doi:10.13371/j.cnki.chin.q.j.m.2025.03.004

Chinese Quarterly Journal of Mathematics >

2025 , Vol. 40 >Issue 3: 271 - 294

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.03.004

Optimal Error Estimates of Multiphysics Finite Element Method for a Nonlinear Poroelasticity Model with Nonlinear Stress-Strain Relation

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School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

GE Zhi-hao (1980-), male, native of Zhoukou, Henan, professor of Henan University, engages in computational mathematics; LI Hai-run (1995-), female, native of Yuncheng, Shanxi, student of Henan University, engages in computational mathematics; LI Ting-ting (1990-), female, native of Zhoukou, Henan, associate professor of Henan University, engages in computational mathematics.

LI Ting-ting (1990-), female, native of Zhoukou, Henan, associate professor of Henan University, engages in computational mathematics.

Accepted date: 2025-06-30

Online published: 2025-09-30

Supported by

Supported by the National Natural Science Foundation of China (Grant Nos. 12371393, 11971150 and 11801143) and Natural Science Foundation of Henan Province (Grant No. 242300421047).

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Abstract

In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation. Firstly, we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields. Secondly, a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically. Thirdly, existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically. Lastly, numerical tests are given to verify the theoretical results.

Key words： Nonlinear poroelasticity model; Multiphysics finite element method; Backward Euler method

Cite this article

GE Zhi-hao, LI Hai-run, LI Ting-ting . Optimal Error Estimates of Multiphysics Finite Element Method for a Nonlinear Poroelasticity Model with Nonlinear Stress-Strain Relation[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(3) : 271 -294 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.004

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