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.

N1 - Funding Information:
The work of F.J. Gaspar wassupported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 705402 , POROSOS. The research of C. Rodrigo was supported in part by the Spanish project FEDER/MCYT MTM2016-75139-R and the DGA (Grupo de referencia APEDIF, ref. E24-17R ). The work of L.T. Zikatanov was partially supported by NSF grants DMS-1522615 and DMS-1720114 . The work of J.H. Adler , X. Hu and P. Ohm was partially supported by NSF grant DMS-1620063 .
Funding Information:
The work of F.J. Gaspar wassupported by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 705402, POROSOS. The research of C. Rodrigo was supported in part by the Spanish project FEDER/MCYTMTM2016-75139-R and the DGA (Grupo de referencia APEDIF, ref. E24-17R). The work of L.T. Zikatanov was partially supported by NSF grants DMS-1522615 and DMS-1720114. The work of J.H. Adler, X. Hu and P. Ohm was partially supported by NSF grant DMS-1620063.
Publisher Copyright:
© 2018 Elsevier B.V.

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.

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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 -