Stability and monotonicity for some discretizations of the Biot’s consolidation model
Stability and monotonicity for some discretizations of the Biot’s consolidation model
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DOI：
10.1016/j.cma.2015.09.019
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发表时间：
2015-04
影响因子：
7.2
通讯作者：
C. Rodrigo;F. Gaspar;Xiaozhe Hu;L. Zikatanov
中科院分区：
文献类型：
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作者：
C. Rodrigo;F. Gaspar;Xiaozhe Hu;L. Zikatanov
考虑了孔隙弹性毕奥固结模型的MINI单元和稳定化P1-P1单元的有限元离散。分析了基于空间离散的全离散模型在时间上的收敛性。我们还解决了与低渗透率和/或小时间步长的压力近似中存在非物理振荡有关的问题。我们表明，即使在1D斯托克斯稳定的有限元对未能提供一个单调的离散化的压力在这样的制度。然后我们引入一个稳定项来消除振荡。我们目前的数值结果证实了稳定的计划的单调行为。
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.