Year: 2014
Type: preprint
Abstract: This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To better describe the multiphysics process of deformation and diffusion for poro-elastic materials, we first present a reformulation of the original model by introducing two pseudo-pressures, one of them is shown to satisfy a diffusion equation, we then propose a time-stepping algorithm which decouples (or couples) the reformulated PDE problem at each time step into two sub-problems, one of which is a generalized Stokes problem for the displacement vector field (of the solid network of the poro-elastic material) along with one pseudo-pressure field and the other is a diffusion problem for the other pseudo-pressure field (of the solvent of the material). In the paper, the Taylor-Hood mixed finite element method combined with the $P_1$-conforming finite element method is used as an example to demonstrate the viability of the proposed multiphysics approach. It is proved that the solutions of the fully discrete finite element methods fulfill a discrete energy law which mimics the differential energy law satisfied by the PDE solution and converges optimally in the energy norm. Moreover, it is showed that the proposed formulation also has a built-in mechanism to overcome so-called "locking phenomenon" associated with the numerical approximations of the poroelasticity model. Numerical experiments are presented to show the performance of the proposed approach and methods and to demonstrate the absence of "locking phenomenon" in our numerical experiments.
Source: arXiv (Cornell University)
Authors: Feng, Xiaobing, Ge, Zhihao, Li, Yukun
Institutions: University of Tennessee at Knoxville, Henan University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: Navier-Stokes方程的稳定化多尺度有限元方法及相关问题的研究, G4222765907, G4425287985, Novel Discontinuous Galerkin Finite Element Methods for Second Order Fully Nonlinear Equations and High Frequency Wave Equations, Numerical Methods and Algorithms for Fully Nonlinear Second Order Evolution Equations with Applications
OpenAlex ID: W263436433