A nonconforming finite element method for the Biot’s consolidation model in poroelasticity

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• 作者：Xiaozhe Hu^a ; ^{xiaozhe.hu@tufts.edu" class="auth_mail" title="E-mail the corresponding author} ; Carmen Rodrigo^b ; ^{carmenr@unizar.es" class="auth_mail" title="E-mail the corresponding author} ; Francisco J. Gaspar^b ; ^{fjgaspar@unizar.es" class="auth_mail" title="E-mail the corresponding author} ; Ludmil T. Zikatanov^c ; ^d ; ^{ludmil@psu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonconforming finite elements ; Stable discretizations ; Monotone discretizations ; Poroelasticity
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：310
• 期：Complete
• 页码：143-154
• 全文大小：547 K

文摘

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.