A nonconforming finite element method for the Biot’s consolidation model in poroelasticity
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摘要
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.
论文关键词:Nonconforming finite elements,Stable discretizations,Monotone discretizations,Poroelasticity
论文评审过程:Received 31 January 2016, Revised 1 May 2016, Available online 21 June 2016, Version of Record 8 September 2016.
论文官网地址:https://doi.org/10.1016/j.cam.2016.06.003