TY - JOUR

T1 - A nonconforming finite element method for the Biot's consolidation model in poroelasticity

AU - Hu, Xiaozhe

AU - Rodrigo, Carmen

AU - Gaspar, Francisco J.

AU - Zikatanov, Ludmil T.

N1 - Funding Information:
Ludmil Zikatanov gratefully acknowledges the support for this work from the Department of Mathematics at Tufts University and the Applied Mathematics Department at University of Zaragoza .
Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2017/1/15

Y1 - 2017/1/15

N2 - A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid flux (Darcy velocity), and the pore pressure, and they are discretized by using the lowest possible approximation order: Crouzeix–Raviart finite elements for the displacements, lowest order Raviart–Thomas-Nédélec elements for the Darcy velocity, and piecewise constant approximation for the pressure. Mass-lumping technique is introduced for the Raviart–Thomas-Nédélec elements in order to eliminate the Darcy velocity and, therefore, reduce the computational cost. We show convergence of the discrete scheme which is implicit in time and use these types of elements in space with and without mass-lumping. Finally, numerical experiments illustrate the convergence of the method and show its effectiveness to avoid spurious pressure oscillations when mass lumping for the Raviart–Thomas-Nédélec elements is used.

AB - A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid flux (Darcy velocity), and the pore pressure, and they are discretized by using the lowest possible approximation order: Crouzeix–Raviart finite elements for the displacements, lowest order Raviart–Thomas-Nédélec elements for the Darcy velocity, and piecewise constant approximation for the pressure. Mass-lumping technique is introduced for the Raviart–Thomas-Nédélec elements in order to eliminate the Darcy velocity and, therefore, reduce the computational cost. We show convergence of the discrete scheme which is implicit in time and use these types of elements in space with and without mass-lumping. Finally, numerical experiments illustrate the convergence of the method and show its effectiveness to avoid spurious pressure oscillations when mass lumping for the Raviart–Thomas-Nédélec elements is used.

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U2 - 10.1016/j.cam.2016.06.003

DO - 10.1016/j.cam.2016.06.003

M3 - Article

AN - SCOPUS:84989922723

VL - 310

SP - 143

EP - 154

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -