Stability and Monotonicity for Some Discretizations of the Biot's Model
Numerical Analysis
2023-07-19 v2
Abstract
We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types of finite elements and implicit Euler method in time. We also address the issue related to the presence of non-physical oscillations in the pressure approximation for low permeabilities and/or small time steps. We show that even in 1D a Stokes-stable finite element pair fails to provide a monotone discretization for the pressure in such regimes. We then introduce a stabilization term which removes the oscillations. We present numerical results confirming the monotone behavior of the stabilized schemes.
Keywords
Cite
@article{arxiv.1504.07150,
title = {Stability and Monotonicity for Some Discretizations of the Biot's Model},
author = {Carmen Rodrigo and Francisco Gaspar and Xiaozhe Hu and Ludmil Zikatanov},
journal= {arXiv preprint arXiv:1504.07150},
year = {2023}
}