Stability and monotonicity for some discretizations of the Biot’s consolidation model
By Carmen Rodrigo, Francisco José Gaspar, Xiaozhe Hu, Ludmil T. Zikatanov. 2015
136 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/51458268b63a19e06bae7376258c3f8f9196b2fb
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In Computational Mechanics
In Computational Theory and Mathematics
Citations in the corpus
- On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics (2017, methodology): “For this stabilized finite element method, discrete inf-sup stability conditions and convergence results were recently derived in [20].”