Paper Info
Title
A nonconforming finite element method for the Biot's consolidation model in poroelasticity.
Abstract
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-Nédélecźelements for the Darcy velocity, and piecewise constant approximation for the pressure. Mass-lumping technique is introduced for the Raviart-Thomas-Nédélecźelements 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-Nédélecźelements is used.
Year
DOI
Venue
2017
10.1016/j.cam.2016.06.003
J. Computational Applied Mathematics
Keywords
Field
DocType
Nonconforming finite elements,Stable discretizations,Monotone discretizations,Poroelasticity
Convergence (routing),Discretization,Mathematical optimization,Mathematical analysis,Finite element method,Poromechanics,Consolidation (soil),Spurious relationship,Piecewise,Mathematics,Biot number
Journal
Volume
Issue
ISSN
310
C
0377-0427
Citations 
PageRank 
References 
5
0.46
7
Authors
4
Name
Order
Citations
PageRank
Xiaozhe Hu14716.68
Carmen Rodrigo2278.69
Francisco José Gaspar3184.66
Ludmil Zikatanov418925.89