Abstract
In this work, we consider the popular P1–RT0–P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation is not uniformly stable with respect to the physical parameters, several issues arise in numerical simulations. For example, when the permeability is small with respect to the mesh size, volumetric locking may occur. To alleviate such problems, we consider a well-known stabilization technique with face bubble functions. We then design a perturbation of the bilinear form, which allows for local elimination of the bubble functions. We further prove that such perturbation is consistent and the resulting scheme has optimal approximation properties for both Biot's model as well as the Stokes’ equations. For the former, the number of degrees of freedom is the same as for the classical P1–RT0–P0 discretization and for the latter (Stokes’ equations) the number of degrees of freedom is the same as for a P1–P0 discretization. We present numerical tests confirming the theoretical results for the poroelastic and the Stokes’ test problems.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 467-484 |
| Number of pages | 18 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 341 |
| DOIs | |
| State | Published - Nov 1 2018 |
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All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications
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New stabilized discretizations for poroelasticity and the Stokes’ equations. / Rodrigo, C.; Hu, X.; Ohm, P.; Adler, J. H.; Gaspar, F. J.; Zikatanov, L. T.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 341, 01.11.2018, p. 467-484.Research output: Contribution to journal › Article
TY - JOUR
T1 - New stabilized discretizations for poroelasticity and the Stokes’ equations
AU - Rodrigo, C.
AU - Hu, X.
AU - Ohm, P.
AU - Adler, J. H.
AU - Gaspar, F. J.
AU - Zikatanov, L. T.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - In this work, we consider the popular P1–RT0–P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation is not uniformly stable with respect to the physical parameters, several issues arise in numerical simulations. For example, when the permeability is small with respect to the mesh size, volumetric locking may occur. To alleviate such problems, we consider a well-known stabilization technique with face bubble functions. We then design a perturbation of the bilinear form, which allows for local elimination of the bubble functions. We further prove that such perturbation is consistent and the resulting scheme has optimal approximation properties for both Biot's model as well as the Stokes’ equations. For the former, the number of degrees of freedom is the same as for the classical P1–RT0–P0 discretization and for the latter (Stokes’ equations) the number of degrees of freedom is the same as for a P1–P0 discretization. We present numerical tests confirming the theoretical results for the poroelastic and the Stokes’ test problems.
AB - In this work, we consider the popular P1–RT0–P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation is not uniformly stable with respect to the physical parameters, several issues arise in numerical simulations. For example, when the permeability is small with respect to the mesh size, volumetric locking may occur. To alleviate such problems, we consider a well-known stabilization technique with face bubble functions. We then design a perturbation of the bilinear form, which allows for local elimination of the bubble functions. We further prove that such perturbation is consistent and the resulting scheme has optimal approximation properties for both Biot's model as well as the Stokes’ equations. For the former, the number of degrees of freedom is the same as for the classical P1–RT0–P0 discretization and for the latter (Stokes’ equations) the number of degrees of freedom is the same as for a P1–P0 discretization. We present numerical tests confirming the theoretical results for the poroelastic and the Stokes’ test problems.
UR - http://www.scopus.com/inward/record.url?scp=85050484423&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85050484423&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2018.07.003
DO - 10.1016/j.cma.2018.07.003
M3 - Article
AN - SCOPUS:85050484423
VL - 341
SP - 467
EP - 484
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0374-2830
ER -