2022/05/15 by Zhihao Ge, Ge, Zhihao, Hairun Li +3
Engineering · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2205.07215
openalex publication_date 2022/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the numerical algorithm for a nonlinear poroelasticity model with nonlinear stress-strain relations. By using variable substitution, the original problem can be reformulated to a new coupled fluid-fluid system, that is, a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields. A new technique is used to get the existence and uniqueness of the solution of the reformulated model and a fully discrete nonlinear finite element method is proposed to solve the model numerically. The multiphysics finite element is used to get the discretization of the space variable and the backward Euler method is taken as the time-stepping method in the fully discrete case. Stability analysis and the error estimation are given for the fully discrete case and numerical test are taken to verify the theoretical results.